Contents for this page | Related topics | |
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1. Charging and discharging capacitors 2. Capacitors in series 3. Capacitors in parallel 4. Additional questions |
Electric charge Electric fields Capacitors Resistors and Ohm's law |
Data Glossary |

Learning Outcomes | ||

After studying this section, you will (a) know how one can use capacitors in a circuit |

1. Charging and discharging capacitors

Consider the circuit shown on the left. When the switch S is open, there is no current flowing through the curcuit, and there is no charge on the capacitor, C.

As soon as the switch is closed, a current starts to flow through the resistor R, and a charge accumulates on the capacitor plates. Intinially, this current has the value E/R, but this value decays with time as the capacitor becomes charged. After a certain time, the capacitor is fully charged, and the potential difference across the plates equals the e.m.f. of the battery. No current flows through the circuit - the charged capacitor acts as an insulator. The behaviours of the current, charge and PD across C are shown in the graphs above (A, B, and C).

The greater the resistance of R and the greater the capacitance of C, the longer it will take to charge the capacitor. (For educators.)

As soon as the switch S is opened, current flows across the resistor R and the ammeter A, (graph E, above left), but in the opposite direction to what was observed when the switch was closed (graph A). This current decays to a value of zero. At the same time, both the charge on C and the PD across C decay to zero (graphs F and G above).

The greater the resistance of R and the greater the capacitance of C, the longer it will take to discharge the capacitor. (For educators.)

2. Capacitors in series

If two or more capacitors having capacitances * C_{1}*,

(For educators: See how this formula is derived.)

3. Capacitors in parallel

If two or more capacitors having capacitances ** C_{1}, C_{2}, ... C_{n}**, are placed in parallel, then the combined capacitance

How can we use capacitors in a circuit? (Click here for a familiar example.) |

4. Additional questions

Time taken to charge and discharge a capacitor

The time, **t**, taken to charge a capacitor with capacitance, ** C** farads, in series with a resistor with resistance

**v = V(1 - e ^{-t/RC})**

where **v** is the potential difference across the capacitor at time **t**, **V** is the final potential difference, and **e** is the base of natural logarithms, (2.718). The product **R x C** is has the dimensions of time, and is known as the

The time, **t**, taken to discharge a capacitor with capacitance, ** C** farads, in series with a resistor with resistance

**v = V e ^{-t/RC}**

Capacitors in series: derivation of formula

Consider the diagram on the left: Let the top plate of capacitor ** C_{1}** acquire a charge +

The negative charge on the bottom plate of ** C_{1}** exactly balances the positive charge on the top plate of

Again, have a good look at the diagram above. The potential difference beween the two points a and c, **V _{ac}** is given by:

Similarly, the potential difference , **V _{cb}** between the points c and b is given by:

But the potential difference applied to the circuit by the battery, **V _{ab}** is the sum of the two potential differences

It follows therefore that the total capacitance ** C_{Tot}** is given by: