Question 10: Describe the process of charging and discharging a capacitor. Give diagram and mathematical expressions for the growth and decay of charge on the capacitor.
Charging of capacitor
A Capacitor is a passive device that stores energy in its Electric Field and returns energy to the circuit whenever required. Many electric circuits consist of capacitors and resistors called RC-circuits. Consider the RC-circuit shown below.
When the switch S1
is closed, a battery of voltage V0
starts charging the capacitor through resistor R. Charge builds up gradually on the plates of the capacitor to the maximum value q0
. If at t = 0, the capacitor is uncharged, it can be shown that after time t, the charge on capacitor is given by the exponential relation,
Where ‘e’ is a constant and its value is 2.718. A graphical representation between q and t is given above.
q=0 at t = 0 and increases gradually to its maximum value q0
. Dividing by C,
If V and V0
denote instantaneous and maximum voltages, respectively, then
Put these values in the above equation
The factor RC is called time constant which is the duration of time for the capacitor in which 63.2% of its maximum value charge is deposited on the plates. This can be seen by putting t = RC,
Putting the value of e,
OR q = 63.2% of q0
Discharging of capacitor
The discharging process is illustrated in the following figures.
When the switch S2
is closed, charge +q on the left plate flow anti-clockwise and neutralize the charge -q on the right plate. The discharging starts from maximum value of charge and decreases gradually to zero. The discharging of the capacitor at any time t can be expressed exponentially by the equation
The graph shows smaller value of RC leads to a more rapid discharge. At t = RC, magnitude of the remaining charge on either plate is,
q = q0
(0.367) = 36.7%(q0
Application of charging and discharging of capacitor
Charging and discharging of capacitors is used in the CDI (Capacitor Discharge Ignition) systems in motorcycles, chain saw (the electric saw used by woodcutters), in the wind screen wipers of automobiles etc.