Charging & Discharging a Capacitor

Charging & Discharging a Capacitor

If the circuit below is set up we can examine the charging and discharging characteristics of a capacitor when it is connected in series with a resistor across a 10 V D.C. supply.

CHARGING

The switch is initially open (down) at t = 0, so that the power supply is short-circuited. At time t = 0.1 s (see Graph 1) the switch is pushed up to the position shown below and current begins to flow whilst the capacitor is charging. The value of the resistor in series with the capacitor controls the charge per second (current) that can flow on to the plates of the capacitor.

Conventional current flow during charge-up

As the charge on the plates of the capacitor builds, the electrostatic repulsion of the charges tends to slow down and then stop any further build up of charge. The capacitor then "stores" charge until the potential difference across its plates is the same voltage as the potential difference of the power supply, in this case 10 V.

The time constant, t, is the time (in seconds) that it takes for the capacitor to charge to 63% of the applied voltage.  It can also be calculated by multiplying the resistance of the series resistor (in W) by the capacitance of the capacitor (in farad).

t=RC

In the example below the theoretical time constant value is

t = RC = 10k  x  10 mF = 10,000   x   10 x 10^-6 = 0.1 s

The time constant, as calculated from the graph is probably closer to 0.13 s.

Note that a capacitor is considered to be "fully-charged" (>99%) after five time constants.

DISCHARGING

When the capacitor is fully charged current no longer flows through the resistor. If we flick the switch again to short-circuit the power supply, the capacitor discharges in the reverse direction, acting as a varying (decreasing) voltage supply that causes current to flow in the opposite direction through the resistor. It discharges with the same time constant that it charges up - if the resistor value remains the same.

Conventional current flow during discharge

CHANGING THE TIME CONSTANT

If we vary the value of the capacitor (or the resistor for that matter) we change the time constant of the RC circuit. In the example below, the value of the capacitor has been increased to 30 mF, three times the initial value. This has the effect of increasing the time constant by a factor of three, i.e. it takes three times longer to charge up but also three times longer to discharge.

From the graph it can be estimated that the time constant (63% mark) is about 0.32 s.

Circuit-makers choose combinations of RC components to get the voltage and time-constant characteristics that they desire. RC circuits are often used as timing elements in circuits.