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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


    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.


    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.