<PAGE>

THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
AMENDED, OR ANY STATE SECURITIES LAWS. THEY MAY NOT BE SOLD OR OFFERED FOR SALE
IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT AS TO THE SECURITIES UNDER
SAID ACT AND ANY APPLICABLE STATE SECURITIES LAWS OR THE AVAILABILITY OF AN
EXEMPTION FROM REGISTRATION UNDER SAID ACT AND ANY APPLICABLE STATE SECURITIES
LAWS.


                                       NO. 1
                             STOCK SUBSCRIPTION WARRANT

                            TO PURCHASE COMMON STOCK OF

                          CONDUCTUS, INC. (THE "COMPANY")

                      DATE OF INITIAL ISSUANCE:  MAY 29, 1998

     THIS CERTIFIES THAT for value received, TRANSAMERICA BUSINESS CREDIT
CORPORATION or its registered assigns (hereinafter called the "Holder") is
entitled to purchase from the Company, at any time during the Term of this
Warrant, Thirty Thousand Four Hundred Fourteen (30,414) shares of common stock,
$0.01 par value, of the Company (the "Common Stock"), at the Warrant Price,
payable as provided herein.  The exercise of this Warrant shall be subject to
the provisions, limitations and restrictions herein contained, and may be
exercised in whole or in part.

SECTION 1.  DEFINITIONS.

     For all purposes of this Warrant, the following terms shall have the
meanings indicated:

     COMMON STOCK - shall mean and include the Company's authorized Common
Stock, $0.01 par value, as constituted at the date hereof.

     EXCHANGE ACT - shall mean the Securities Exchange Act of 1934, as amended
from time to time.

     SECURITIES ACT - the Securities Act of 1933, as amended.

     TERM OF THIS WARRANT - shall mean the period beginning on the date of
initial issuance hereof and ending on June 1, 2003.

     WARRANT PRICE - $4.11 per share, subject to adjustment in accordance with
Section 5 hereof.

     WARRANTS - this Warrant and any other Warrant or Warrants issued in
connection with a Commitment Letter dated April 22, 1998 executed by the Company
and Transamerica Business Credit Corporation (the "Commitment Letter") to the
original holder of this Warrant, or any transferees from such original holder or
this Holder.

     WARRANT SHARES - shares of Common Stock purchased or purchasable by the
Holder of this Warrant upon the exercise hereof.

<PAGE>

SECTION 2.  EXERCISE OF WARRANT.

     2.1. PROCEDURE FOR EXERCISE OF WARRANT.  To exercise this Warrant in whole
or in part (but not as to any fractional share of Common Stock), the Holder
shall deliver to the Company at its office referred to in Section 12 hereof at
any time and from time to time during the Term of this Warrant: (i) the Notice
of Exercise in the form attached hereto, (ii) cash, certified or official bank
check payable to the order of the Company, wire transfer of funds to the
Company's account, or evidence of any indebtedness of the Company to the Holder
(or any combination of any of the foregoing) in the amount of the Warrant Price
for each share being purchased, and (iii) this Warrant.  Notwithstanding any
provisions herein to the contrary, if the Current Market Price (as defined in
Section 5) is greater than the Warrant Price (at the date of calculation, as set
forth below), in lieu of exercising this Warrant as hereinabove permitted, the
Holder may elect to receive shares of Common Stock equal to the value (as
determined below) of this Warrant (or the portion thereof being canceled) by
surrender of this Warrant at the office of the Company referred to in Section 12
hereof, together with the Notice of Exercise, in which event the Company shall
issue to the Holder that number of shares of Common Stock computed using the
following formula:

                                CS = WCS x (CMP-WP)
                                -------------------
                                        CMP

Where

     CS   equals the number of shares of Common Stock to be issued to the Holder

     WCS  equals the number of shares of Common Stock purchasable under the
          Warrant or, if only a portion of the Warrant is being exercised, the
          portion of the Warrant being exercised (at the date of such
          calculation)

     CMP  equals the Current Market Price (at the date of such calculation)

     WP   equals the Warrant Price (as adjusted to the date of such calculation)

In the event of any exercise of the rights represented by this Warrant, a
certificate or certificates for the shares of Common Stock so purchased,
registered in the name of the Holder or such other name or names as may be
designated by the Holder, shall be delivered to the Holder hereof within a
reasonable time, not exceeding fifteen (15) days, after the rights represented
by this Warrant shall have been so exercised; and, unless this Warrant has
expired, a new Warrant representing the number of shares (except a remaining
fractional share), if any, with respect to which this Warrant shall not then
have been exercised shall also be issued to the Holder hereof within such time. 
The person in whose name any certificate for shares of Common Stock is issued
upon exercise of this Warrant shall for all purposes be deemed to have become
the holder of record of such shares on the date on which the Warrant was
surrendered and payment of the Warrant Price and any applicable taxes was made,
irrespective of the date of delivery of such certificate, except that, if the
date of such surrender and payment is a date when the stock transfer books of
the Company are closed, such person shall be deemed to have become the holder of
such shares at the close of business on the next succeeding date on which the
stock transfer books are open.

     2.2. TRANSFER RESTRICTION LEGEND.  Each certificate for Warrant Shares
shall bear the following legend (and any additional legend required by (i) any
applicable state securities laws and (ii) 

                                      - 2 -

<PAGE>

any securities exchange upon which such Warrant Shares may, at the time of 
such exercise, be listed) on the face thereof unless at the time of exercise 
such Warrant Shares shall be registered under the Securities Act:

     "The shares represented by this certificate have not been registered
     under the Securities Act of 1933, as amended, and may not be sold or
     transferred in the absence of such registration or an exemption
     therefrom under said Act."

Any certificate issued at any time in exchange or substitution for any
certificate bearing such legend (except a new certificate issued upon completion
of a public distribution under a registration statement of the securities
represented thereby) shall also bear such legend unless, in the opinion of
counsel for the holder thereof (which counsel shall be reasonably satisfactory
to counsel for the Company) the securities represented thereby are not, at such
time, required by law to bear such legend.


SECTION 3.  COVENANTS AS TO COMMON STOCK.  The Company covenants and agrees that
all shares of Common Stock that may be issued upon the exercise of the rights
represented by this Warrant will, upon issuance, be validly issued, fully paid
and nonassessable, and free from all taxes, liens and charges with respect to
the issue thereof.  The Company further covenants and agrees that it will pay
when due and payable any and all federal and state taxes which may be payable in
respect of the issue of this Warrant or any Common Stock or certificates
therefor issuable upon the exercise of this Warrant.  The Company further
covenants and agrees that the Company will at all times have authorized and
reserved, free from preemptive rights, a sufficient number of shares of Common
Stock to provide for the exercise of the rights represented by this Warrant. 
The Company further covenants and agrees that if any shares of capital stock to
be reserved for the purpose of the issuance of shares upon the exercise of this
Warrant require registration with or approval of any governmental authority
under any federal or state law before such shares may be validly issued or
delivered upon exercise, then the Company will in good faith and as
expeditiously as possible endeavor to secure such registration or approval, as
the case may be.  If and so long as the Common Stock issuable upon the exercise
of this Warrant is listed on any national securities exchange, the Company will,
if permitted by the rules of such exchange, list and keep listed on such
exchange, upon official notice of issuance, all shares of such Common Stock
issuable upon exercise of this Warrant.

SECTION 4.  ADJUSTMENT OF NUMBER OF SHARES. Upon each adjustment of the Warrant
Price as provided in Section 5, the Holder shall thereafter be entitled to
purchase, at the Warrant Price resulting from such adjustment, the number of
shares (calculated to the nearest tenth of a share) obtained by multiplying the
Warrant Price in effect immediately prior to such adjustment by the number of
shares purchasable pursuant hereto immediately prior to such adjustment and
dividing the product thereof by the Warrant Price resulting from such
adjustment.

SECTION 5.  Adjustment of Warrant Price.  The Warrant Price shall be subject to
adjustment from time to time as follows:

 If, at any time during the Term of this Warrant, the number of shares of Common
Stock outstanding is increased by a stock dividend payable in shares of Common
Stock or by a subdivision or split-up of shares of Common Stock, then, following
the record date fixed for the determination of holders of Common Stock entitled
to receive such stock dividend, subdivision or split-up, the Warrant Price shall
be appropriately decreased so that the number of shares of Common Stock issuable
upon the exercise hereof shall be increased in proportion to such increase in
outstanding shares.

                                      - 3 -

<PAGE>

     (ii)  If, at any time during the Term of this Warrant, the number of shares
of Common Stock outstanding is decreased by a combination of the outstanding
shares of Common Stock, then, following the record date for such combination,
the Warrant Price shall appropriately increase so that the number of shares of
Common Stock issuable upon the exercise hereof shall be decreased in proportion
to such decrease in outstanding shares.

     (iii) In case, at any time during the Term of this Warrant, the Company
shall declare a cash dividend upon its Common Stock payable otherwise than out
of earnings or earned surplus or shall distribute to holders of its Common Stock
shares of its capital stock (other than Common Stock), stock or other securities
of other persons, evidences of indebtedness issued by the Company or other
persons, assets (excluding cash dividends and distributions) or options or
rights (excluding options to purchase and rights to subscribe for Common Stock
or other securities of the Company convertible into or exchangeable for Common
Stock), then, in each such case, immediately following the record date fixed for
the determination of the holders of Common Stock entitled to receive such
dividend or distribution, the Warrant Price in effect thereafter shall be
determined by multiplying the Warrant Price in effect immediately prior to such
record date by a fraction of which the numerator shall be an amount equal to the
difference of (x) the Current Market Price of one share of Common Stock minus
(y) the fair market value (as determined by the Board of Directors of the
Company, whose determination shall be conclusive) of the stock, securities,
evidences of indebtedness, assets, options or rights so distributed in respect
of one share of Common Stock, and of which the denominator shall be such Current
Market Price.

     (iv)  All calculations under this Section 5 shall be made to the nearest
cent or to the nearest one-tenth (1/10) of a share, as the case may be.

     (v)  For the purpose of any computation pursuant to this Section 5, the
Current Market Price at any date of one share of Common Stock shall be deemed to
be the average of the daily closing prices for the 15 consecutive business days
ending on the last business day before the day in question (as adjusted for any
stock dividend, split, combination or reclassification that took effect during
such 15 business day period).  The closing price for each day shall be the last
reported sales price regular way or, in case no such reported sales took place
on such day, the average of the last reported bid and asked prices regular way,
in either case on the principal national securities exchange on which the Common
Stock is listed or admitted to trading or as reported by Nasdaq (or if the
Common Stock is not at the time listed or admitted for trading on any such
exchange or if prices of the Common Stock are not reported by Nasdaq then such
price shall be equal to the average of the last reported bid and asked prices on
such day as reported by The National Quotation Bureau Incorporated or any
similar reputable quotation and reporting service, if such quotation is not
reported by The National Quotation Bureau Incorporated); provided, however, that
if the Common Stock is not traded in such manner that the quotations referred to
in this clause (v) are available for the period required hereunder, the Current
Market Price shall be determined in good faith by the Board of Directors of the
Company or, if such determination cannot be made, by a nationally recognized
independent investment banking firm selected by the Board of Directors of the
Company (or if such selection cannot be made, by a nationally recognized
independent investment banking firm selected by the American Arbitration
Association in accordance with its rules).

     (vi)  Whenever the Warrant Price shall be adjusted as provided in Section
5, the Company shall prepare a statement showing the facts requiring such
adjustment and the Warrant Price that shall be in effect after such adjustment. 
The Company shall cause a copy of such statement to be sent by mail, first 

                                      - 4 -

<PAGE>

class postage prepaid, to each Holder of this Warrant at its, his or her 
address appearing on the Company's records.  Where appropriate, such copy may 
be given in advance and may be included as part of the notice required to be 
mailed under the provisions of subsection (viii) of this Section 5.

     (vii)  Adjustments made pursuant to clauses (i), (ii) and (iii) above shall
be made on the date such dividend, subdivision, split-up, combination or
distribution, as the case may be, is made, and shall become effective at the
opening of business on the business day next following the record date for the
determination of stockholders entitled to such dividend, subdivision, split-up,
combination or distribution.

     (viii) In the event the Company shall propose to take any action of the
types described in clauses (i), (ii), or (iii) of this Section 5, the Company
shall forward, at the same time and in the same manner, to the Holder of this
Warrant such notice, if any, which the Company shall give to the holders of
capital stock of the Company.

     (ix)  In any case in which the provisions of this Section 5 shall require
that an adjustment shall become effective immediately after a record date for an
event, the Company may defer until the occurrence of such event issuing to the
Holder of all or any part of this Warrant which is exercised after such record
date and before the occurrence of such event the additional shares of capital
stock issuable upon such exercise by reason of the adjustment required by such
event over and above the shares of capital stock issuable upon such exercise
before giving effect to such adjustment exercise; provided, however, that the
Company shall deliver to such Holder a due bill or other appropriate instrument
evidencing such Holder's right to receive such additional shares upon the
occurrence of the event requiring such adjustment.

SECTION 6.  OWNERSHIP.

     6.1. OWNERSHIP OF THIS WARRANT.  The Company may deem and treat the person
in whose name this Warrant is registered as the holder and owner hereof
(notwithstanding any notations of ownership or writing hereon made by anyone
other than the Company) for all purposes and shall not be affected by any notice
to the contrary until presentation of this Warrant for registration of transfer
as provided in this Section 6.

     6.2. TRANSFER AND REPLACEMENT.  This Warrant and all rights hereunder are
transferable in whole or in part upon the books of the Company by the Holder
hereof in person or by duly authorized attorney, and a new Warrant or Warrants,
of the same tenor as this Warrant but registered in the name of the transferee
or transferees (and in the name of the Holder, if a partial transfer is
effected) shall be made and delivered by the Company upon surrender of this
Warrant duly endorsed, at the office of the Company referred to in Section 12
hereof.  Upon receipt by the Company of evidence reasonably satisfactory to it
of the loss, theft or destruction, and, in such case, of indemnity or security
reasonably satisfactory to it, and upon surrender of this Warrant if mutilated,
the Company will make and deliver a new Warrant of like tenor, in lieu of this
Warrant; provided that if the Holder hereof is an instrumentality of a state or
local government or an institutional holder or a nominee for such an
instrumentality or institutional holder an irrevocable agreement of indemnity by
such Holder shall be sufficient for all purposes of this Section 6, and no
evidence of loss or theft or destruction shall be necessary.  This Warrant shall
be promptly cancelled by the Company upon the surrender hereof in connection
with any transfer or replacement.  Except as otherwise provided above, in the
case of the loss, theft or destruction of a Warrant, the Company shall pay all
expenses, taxes and other charges payable in connection with any transfer or
replacement of this Warrant, other than stock transfer taxes (if any) payable in
connection 

                                      - 5 -

<PAGE>

with a transfer of this Warrant, which shall be payable by the Holder.  Holder 
will not transfer this Warrant and the rights hereunder except in compliance 
with federal and state securities laws.

SECTION 7.  MERGERS, CONSOLIDATION, SALES.  In the case of any proposed
consolidation or merger of the Company with another entity, or the proposed sale
of all or substantially all of its assets to another person or entity, or any
proposed reorganization or reclassification of the capital stock of the Company,
then, as a condition of such consolidation, merger, sale, reorganization or
reclassification, lawful and adequate provision shall be made whereby the Holder
of this Warrant shall thereafter have the right to receive upon the basis and
upon the terms and conditions specified herein, in lieu of the shares of the
Common Stock of the Company immediately theretofore purchasable hereunder, such
shares of stock, securities or assets as may (by virtue of such consolidation,
merger, sale, reorganization or reclassification) be issued or payable with
respect to or in exchange for the number of shares of such Common Stock
purchasable hereunder immediately before such consolidation, merger, sale,
reorganization or reclassification.  In any such case appropriate provision
shall be made with respect to the rights and interests of the Holder of this
Warrant to the end that the provisions hereof shall thereafter be applicable as
nearly as may be, in relation to any shares of stock, securities or assets
thereafter deliverable upon the exercise of this Warrant.

SECTION 8.  NOTICE OF DISSOLUTION OR LIQUIDATION.  In case of any distribution
of the assets of the Company in dissolution or liquidation (except under
circumstances when the foregoing Section 7 shall be applicable), the Company
shall give notice thereof to the Holder hereof and shall make no distribution to
shareholders until the expiration of thirty (30) days from the date of mailing
of the aforesaid notice and, in any case, the Holder hereof may exercise this
Warrant within thirty (30) days from the date of the giving of such notice, and
all rights herein granted not so exercised within such thirty-day period shall
thereafter become null and void.

SECTION 9.  NOTICE OF EXTRAORDINARY DIVIDENDS.  If the Board of Directors of the
Company shall declare any dividend or other distribution on its Common Stock
except out of earned surplus or by way of a stock dividend payable in shares of
its Common Stock, the Company shall mail notice thereof to the Holder hereof not
less than thirty (30) days prior to the record date fixed for determining
shareholders entitled to participate in such dividend or other distribution, and
the Holder hereof shall not participate in such dividend or other distribution
unless this Warrant is exercised prior to such record date.  The provisions of
this Section 9 shall not apply to distributions made in connection with
transactions covered by Section 7.

SECTION 10.  FRACTIONAL SHARES.  Fractional shares shall not be issued upon the
exercise of this Warrant but in any case where the Holder would, except for the
provisions of this Section 10, be entitled under the terms hereof to receive a
fractional share upon the complete exercise of this Warrant, the Company shall,
upon the exercise of this Warrant for the largest number of whole shares then
called for, pay a sum in cash equal to the excess of the value of such
fractional share (determined in such reasonable manner as may be prescribed in
good faith by the Board of Directors of the Company) over the Warrant Price for
such fractional share.

SECTION 11.  SPECIAL ARRANGEMENTS OF THE COMPANY.  The Company covenants and
agrees that during the Term of this Warrant, unless otherwise approved by the
Holder of this Warrant:

                                      - 6 -

<PAGE>

     11.1.     WILL RESERVE SHARES.  The Company will reserve and set apart and
have available for issuance at all times, free from preemptive or other
preferential rights, the number of shares of authorized but unissued Common
Stock deliverable upon the exercise of this Warrant.

     11.2.     WILL NOT AMEND CERTIFICATE.  The Company will not amend its
Certificate of Incorporation to eliminate as an authorized class of capital
stock that class denominated as "Common Stock" on the date hereof.

     11.3.     WILL BIND SUCCESSORS.  This Warrant shall be binding upon any
corporation or other person or entity succeeding to the Company by merger,
consolidation or acquisition of all or substantially all of the Company's
assets.

SECTION 12.  NOTICES.  Any notice or other document required or permitted to be
given or delivered to the Holder shall be delivered at, or sent by certified or
registered mail to, the Holder at Transamerica Technology Finance Division, 76
Batterson Park Road, Farmington, Connecticut 06032, Attention:  Assistant Vice
President, Lease Administration, with a copy to the Lender at Riverway II, West
Office Tower, 9399 West Higgins Road, Rosemont, Illinois  60018, Attention: 
Legal Department or to such other address as shall have been furnished to the
Company in writing by the Holder.  Any notice or other document required or
permitted to be given or delivered to the Company shall be delivered at, or sent
by certified or registered mail to, the Company at 969 West Maude Avenue,
Sunnyvale, California, 94086, Attention: Chief Financial Officer or to such
other address as shall have been furnished in writing to the Holder by the
Company. Any notice so addressed and mailed by registered or certified mail
shall be deemed to be given when so mailed. Any notice so addressed and
otherwise delivered shall be deemed to be given when actually received by the
addressee.

SECTION 13.  NO RIGHTS AS STOCKHOLDER; LIMITATION OF LIABILITY.  This Warrant
shall not entitle the Holder to any of the rights of a shareholder of the
Company except upon exercise in accordance with the terms hereof.  No provision
hereof, in the absence of affirmative action by the Holder to purchase shares of
Common Stock, and no mere enumeration herein of the rights or privileges of the
Holder, shall give rise to any liability of the Holder for the Warrant Price
hereunder or as a shareholder of the Company, whether such liability is asserted
by the Company or by creditors of the Company.

SECTION 14.  LAW GOVERNING.  THE VALIDITY, INTERPRETATION, AND ENFORCEMENT OF
THIS WARRANT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF
THE STATE OF ILLINOIS WITHOUT GIVING EFFECT TO THE CONFLICT OF LAW PRINCIPLES
THEREOF.

SECTION 15.  MISCELLANEOUS.  This Warrant and any provision hereof may be
changed, waived, discharged or terminated only by an instrument in writing
signed by both parties (or any respective predecessor in interest thereof).  The
headings in this Warrant are for purposes of reference only and shall not affect
the meaning or construction of any of the provisions hereof

                                      - 7 -

<PAGE>

     IN WITNESS WHEREOF, the Company has caused this Warrant to be signed by its
duly authorized officer this _______ day of _________, 199__.



                                              CONDUCTUS, INC.
[CORPORATE SEAL]

                                              By: 
                                                  ----------------------------

                                              Title:
                                                     -------------------------

                                      - 8 -

<PAGE>

                             FORM OF NOTICE OF EXERCISE

                  [TO BE SIGNED ONLY UPON EXERCISE OF THE WARRANT]

                      TO BE EXECUTED BY THE REGISTERED HOLDER
                           TO EXERCISE THE WITHIN WARRANT


     The undersigned hereby exercises the right to purchase _________ shares of
Common Stock which the undersigned is entitled to purchase by the terms of the
within Warrant according to the conditions thereof, and herewith

[check one]
                         / /  makes payment of $__________ therefor; or

                        / /  directs the Company to issue ______ shares, and to 
                             withhold ____ shares in lieu of payment of the 
                             Warrant Price, as described in Section 2.1 of the 
                             Warrant.

All shares to be issued pursuant hereto shall be issued in the name of and the
initial address of such person to be entered on the books of the Company shall
be:



     The shares are to be issued in certificates of the following denominations:




                                               ---------------------------
                                               [Type Name of Holder]


                                               By: 
                                               ---------------------------

                                               Title:
                                               ---------------------------


Dated:__________________________

                                      - 9 -

<PAGE>

                                 FORM OF ASSIGNMENT
                                      (ENTIRE)

                [TO BE SIGNED ONLY UPON TRANSFER OF ENTIRE WARRANT]

                      TO BE EXECUTED BY THE REGISTERED HOLDER
                           TO TRANSFER THE WITHIN WARRANT

     FOR VALUE RECEIVED ___________________________ hereby sells, assigns and
transfers unto _______________________________ all rights of the undersigned
under and pursuant to the within Warrant, and the undersigned does hereby
irrevocably constitute and appoint _______________________________ Attorney to
transfer the said Warrant on the books of the Company, with full power of
substitution.




                                               -------------------------------
                                               [Type Name of Holder]


                                               By: 
                                                   ---------------------------

                                               Title:
                                                      ------------------------

Dated:________________________


NOTICE

     The signature to the foregoing Assignment must correspond to the name as
written upon the face of the within Warrant in every particular, without
alteration or enlargement or any change whatsoever.

                                      - 10 -

<PAGE>

                                 FORM OF ASSIGNMENT
                                     (PARTIAL)

                [To be signed only upon partial transfer of Warrant]

                      TO BE EXECUTED BY THE REGISTERED HOLDER
                           TO TRANSFER THE WITHIN WARRANT

     FOR VALUE RECEIVED _________________________ hereby sells, assigns and
transfers unto _______________________________ (i) the rights of the undersigned
to purchase ___ shares of Common Stock under and pursuant to the within Warrant,
and (ii) on a non-exclusive basis, all other rights of the undersigned under and
pursuant to the within Warrant, it being understood that the undersigned shall
retain, severally (and not jointly) with the transferee(s) named herein, all
rights assigned on such non-exclusive basis.  The undersigned does hereby
irrevocably constitute and appoint __________________________ Attorney to
transfer the said Warrant on the books of the Company, with full power of
substitution.




                                               -------------------------------
                                               [Type Name of Holder]


                                               By: 
                                                   ---------------------------

                                               Title:
                                                      ------------------------

Dated:
      --------------------------


NOTICE

     The signature to the foregoing Assignment must correspond to the name as
written upon the face of the within Warrant in every particular, without
alteration or enlargement or any change whatsoever.

                                      - 11 -