#### The charging and discharging, Time constant

**Possible Experiments**
- Charging a capacitor by a DC power supply and discharging by a resistor,
- Measurement of time constant of the circuit: τ=RC

**Standard Equipment**
DC power supply, ampermeter, voltmeter, resistor and capacitor set, connection cables.

**Technical Information **
Charging:

If the capacitor in the figure is empty at t=0 it starts charging after
S_{1} is closed (S_{2} open). The voltage across the capacitor increases in time (τ=RC) with a time constant of but the current reduces from its initial value. As current drops to zero the voltage across capacitor reaches V, fully charged case. In that case the relationship: Q=CV is applicable. According to Kirchoff's law,
V=IR+Q/C. If the time derivative is taken one gets the solution of this equation as:
Q=CV(1-e^{-t/τ}). Since I=dQ/dt, the current becomes:
I=V/R e^{-t/τ}. One can see from these equations that as charge increases in time the current reduces.

Discharging:

If S_{2} is closed and S_{1} is open after fully charging, the current directs in opposite direction and capacitor gets emptier by the resistor. In that case the current is given as: I=-V_{c0}/R e^{-t/τ}, minus sign showing it is in opposite direction and V_{c0} is the voltage just before discharging starts.

The currents are measured by multimeters (mA range) as charging and discharging as a function of time and their graphs are obtained. The log-time graphs of these functions give time constant. The calculated value is then compared with actual value.