A capacitor of capacitance C it discharging through a resistor of resistance R I

Question

A capacitor of capacitance C it discharging through a resistor of resistance R In terms of the time constant tau = RC. when will the charge on the capacitor be half its initial value? When will the energy stored in the capacitor be half its initial value? At what rate PR is thermal energy produced in the resistor during the discharging process? At what rate Pc is stored energy lost by the capacitor during the discharging process? The circuit in Fig. 28.15 consists of an ideal battery with emf E = 12 V, two resistors with resistances R1 = 4.0 Ohm and R2 = 6.0 Ohm, and an initially uncharged capacitor with capacitance C = 6.0 muC. The circuit is completed when switch S is closed at time t = 0. At time t = 2.0tau, what is the potential difference across the capacitor? At time t = 2.0tau. what are the potential differences VR and VR1 across the two resistors? Do those potential differences increase, decrease, or remain the same while the capacitor is being charged? FIGURE 28 - 15 When switch S is closed, the circuit it complete and the battery begins to charge the capacitor.

Explanation / Answer

a. apply Q = Qo(1-e-t/RC)

1-e^-t/RC = 0.5

e^-t/RC = 0.5

-t/RC = ln (0.5) = =0.693

t = 0.693 time constants
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