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• # EE - 209 Charging/Discharging of Capacitors

#### 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 S1 is closed (S2 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 S2 is closed and S1 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=-Vc0/R e-t/τ, minus sign showing it is in opposite direction and Vc0 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.

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