Capacitor

## Contents

1.Introduction to Capacitors

2.How Capacitors works

3.capacitance

4.Applications

5.Charging Capacitors

6.discharging Capacitors

7.tips from the author

### Introduction to Capacitors

☀Just like the Resistor, the Capacitor, sometimes referred to as a condenser, is a simple passive device that is used to “store electricity” on its plates.

☀In its basic form, a capacitor consists of two or more parallel conductive (metal) plates which are not connected or touching each other, but are electrically separated either by air or by some form of a good insulating material such as waxed paper, mica, ceramic, plastic or some form of a liquid gel as used in electrolytic capacitors. The insulating layer between a capacitors plates is commonly called the Dielectric.Due to this insulating layer, DC current can not flow through the capacitor as it blocks it allowing instead a voltage to be present across the plates in the form of an electrical charge.

☀In the exam, we need to know several terms related to capacitor such as: capacitance **C**(usually a very small number) or time constant **t**.

### How Capacitors works

When you connect a capacitor to a battery, here's what happens:

☀ The plate on the capacitor that attaches to the **negative** terminal of the battery **accepts** electrons that the battery is producing.

☀ The plate on the capacitor that attaches to the **positive** terminal of the battery **loses** electrons to the battery.

Once it's charged, the capacitor has the same voltage as the battery (1.5 volts on the battery means 1.5 volts on the capacitor).

### capacitance

A capacitor's storage potential, or capacitance, is measured in units called farads. A 1-farad capacitor can store one coulomb (coo-lomb) of charge at 1 volt. A coulomb is 6.25e18 (6.25 \* 10^18, or 6.25 billion billion) electrons. One amp represents a rate of electron flow of 1 coulomb of electrons per second, so a 1-farad capacitor can hold 1 amp-second of electrons at 1 volt.

A 1-farad capacitor would typically be pretty big. It might be as big as a can of tuna or a 1-liter soda bottle, depending on the voltage it can handle. For this reason, capacitors are typically measured in **microfarads**

 To get some perspective on how big a farad is, think about this:

☀ A standard alkaline AA battery holds about 2.8 amp-hours.

☀ That means that a AA battery can produce 2.8 amps for an hour at 1.5 volts (about 4.2 watt-hours -- a AA battery can light a 4-watt bulb for a little more than an hour).

☀ Let's call it 1 volt to make the math easier. To store one AA battery's energy in a capacitor, you would need 3,600 \* 2.8 = 10,080 farads to hold it, because an amp-hour is 3,600 amp-seconds.

### Applications

☀ difference between a capacitor and a battery is that a capacitor can dump its entire charge in a tiny fraction of a second, where a battery would take minutes to completely discharge. That's why the electronic flash on a camera uses a capacitor -- the battery charges up the flash's capacitor over several seconds, and then the capacitor dumps the full charge into the flash tube almost instantly. This can make a large, charged capacitor extremely dangerous -- flash units and TVs have warnings about opening them up for this reason. They contain big capacitors that can, potentially, kill you with the charge they contain.

☀ A capacitor can block DC voltage. If you hook a small capacitor to a battery, then no current will flow between the poles of the battery once the capacitor charges. However, any alternating current (AC) signal flows through a capacitor unimpeded. That's because the capacitor will charge and discharge as the alternating current fluctuates, making it appear that the alternating current is flowing.

### Charging Capacitors

☀ When a voltage source is applied to a capacitor, C charges up through the resistance, R

☀ When an increasing DC voltage is applied to a discharged Capacitor, the capacitor draws a charging current and “charges up”, and when the voltage is reduced, the capacitor discharges in the opposite direction. Because capacitors are able to store electrical energy they act like small batteries and can store or release the energy as required.

☀ The charge on the plates of the capacitor is given as: **Q = CV**. This charging (storage) and discharging (release) of a capacitors energy is never instant but takes a certain amount of time to occur with the time taken for the capacitor to charge or discharge to within a certain percentage of its maximum supply value being known as its **Time Constant ( τ ).**

☀ If a resistor is connected in series with the capacitor forming an RC circuit, the capacitor will charge up gradually through the resistor until the voltage across the capacitor reaches that of the supply voltage. The time also called the transient response, required for the capacitor to fully charge is equivalent to about 5 time constants or **5T.**

☀ The capacitor now starts to charge up as shown, with the rise in the RC charging curve steeper at the beginning because the charging rate is fastest at the start and then tapers off as the capacitor takes on additional charge at a slower rate.

☀ As the capacitor charges up, the potential difference across its plates slowly increases with the actual time taken for the charge on the capacitor to reach 63% of its maximum possible voltage, in our curve 0.63Vs being known as one Time Constant, ( T ).

This 0.63Vs voltage point is given the abbreviation of 1T, (one time constant).

☀ The capacitor continues charging up and the voltage difference between Vs and Vcreduces, so to does the circuit current, i. Then at its final condition greater than five time constants ( 5T ) when the capacitor is said to be fully charged, t = ∞, i = 0, q = Q = CV. Then at infinity the current diminishes to **zero**, the capacitor acts like an open circuit condition therefore, the voltage drop is entirely across the capacitor.

### discharging Capacitors

☀ When a voltage source is removed from a fully charged RC circuit, the capacitor, C will discharge back through the resistance, R

☀ As with the previous RC charging circuit, in a RC Discharging Circuit, the time constant ( τ ) is still equal to the value of 63%. Then for a RC discharging circuit that is initially fully charged, the voltage across the capacitor after one time constant, 1T, has dropped to **63%**of its initial value which is 1 – 0.63 = 0.37 or **37%** of its final value.

☀ So now this is given as the time taken for the capacitor to discharge down to within 37% of its fully discharged value which will be zero volts (fully discharged), and in our curve this is given as 0.37Vc.

☀ As the capacitor discharges, it loses its charge at a declining rate. At the start of discharge the initial conditions of the circuit, are t = 0, i = 0 and q = Q. The voltage across the capacitors plates is equal to the supply voltage and Vc = Vs. As the voltage across the plates is at its highest value maximum discharge current flows around the circuit.

☀ With the switch closed, the capacitor now starts to discharge as shown, with the decay in the RC discharging curve steeper at the beginning because the discharging rate is fastest at the start and then tapers off as the capacitor looses charge at a slower rate. As the discharge continues, Vc goes down and there is less discharge current.

☀ As with the previous charging circuit the voltage across the capacitor, C is equal to 0.5Vcat 0.7T with the steady state fully discharged value being finally reached at 5T.

### tips from the author

☀ Remember to mention sth specifically in the "\* questions" rather than mention it vaguely, bring the key words such as "exponentially" with you.

☀ Three Expressions for the Energy stored by a Capacitor: W=Q2/2CW=1/2QV W=1/2CV2

☀ related Capacitor to electric field might get you extra mark.

☀ Also remember how to find the capacitance of a Capacitor by discharging it and know how to use a diagram to support the method.