<PAGE>
 
                                                                   EXHIBIT 12(b)

                        TEXAS UTILITIES ELECTRIC COMPANY

              COMPUTATION OF RATIO OF EARNINGS TO FIXED CHARGES,
                 AND TO FIXED CHARGES AND PREFERRED DIVIDENDS
<TABLE>
<CAPTION>
 
                                                                       Year Ended December 31,
                                                                       -----------------------                            
                                                     1997        1996          1995         1994         1993
                                                                 Thousands of Dollars, Except Ratios
<S>                                                <C>          <C>           <C>          <C>          <C>
EARNINGS:
  Net income                                       $  771,874   $  862,695    $  452,631    $  658,192   $  476,526
  Add: Total income taxes                             409,546      405,499       212,953       342,687      241,740
       Fixed charges (see detail below)               618,773      649,295       655,678       688,194      715,609
                                                   ----------   ----------    ----------    ----------   ----------
           Total earnings                          $1,800,193   $1,917,489    $1,321,262    $1,689,073   $1,433,875
                                                   ==========   ==========    ==========    ==========   ==========
 
FIXED CHARGES:
  Interest on mortgage bonds                         $439,398   $  486,791    $  526,977    $  567,363   $  610,999
  Interest on other long-term debt                     22,124       26,456        44,071        32,183       45,787
  Amortization of debt discount, (premium)
     and expense                                       11,053       11,067         9,959         8,615        6,493
  Amortization of loss on reacquired debt              24,149       22,520        19,547        17,608       12,471
  Other interest charges                               30,542       48,872        28,994        36,408       10,222
  Preferred trust securities distributions             69,701       33,001         1,801            --           --
  Rentals representative of the interest factor        21,806       20,588        24,329        26,017       29,637
                                                   ----------   ----------    ----------    ----------   ----------
           Total fixed charges                     $  618,773   $  649,295    $  655,678    $  688,194   $  715,609
                                                   ==========   ==========    ==========    ==========   ==========
 
Preferred dividends*                                   15,439       68,988        93,489       143,233      168,465
                                                   ----------   ----------    ----------    ----------   ----------
           Fixed charges and preferred
             dividends                             $  634,212   $  718,283    $  749,167    $  831,427   $  884,074
                                                   ==========   ==========    ==========    ==========   ==========
 
RATIO OF EARNINGS TO FIXED CHARGES                        2.9          3.0           2.0           2.5          2.0
                                                   ==========   ==========    ==========    ==========   ==========
 
RATIO OF EARNINGS TO FIXED CHARGES
  AND PREFERRED DIVIDENDS                                 2.8          2.7           1.8           2.0          1.6
                                                   ==========   ==========    ==========    ==========   ==========
 
</TABLE>

 . Preferred dividends represent (1) the portion of preferred dividends
  deductible for federal income tax purposes, plus (2) the balance of preferred
  dividend requirements multiplied by the ratio of pre-tax income to net income.