In the circuit in the figure below, the emf equals 5.83 V and has negligible int

Question

In the circuit in the figure below, the emf equals 5.83 V and has negligible internal resistance. The capacitance equals 1.31 µF and the resistance equals 1.88 M. Switch S has been closed for a long time. Switch S is opened. After a time interval equal to one time constant of the circuit has elapsed, find the following.

(a) the charge on the capacitor plate on the right
µC

(b) the rate at which the charge is increasing
µC/s

(c) the current
µC/s

(d) the power supplied by the battery
µW

(e) the power delivered to the resistor
µW

(f) the rate at which the energy stored in the capacitor is increasing
µW

Explanation / Answer

In a RC circuit charge as a function of time for charging is given by

Q=Qmax(1-e-t/T)

at t=T

Q=(5.83*1.31)(1-e-1)

Q=4.83 uC

b)

In a RC circuit current as a function of time is given by

I=Imaxe-t/T

I=(5.83/1.88*106)e-1

I=dQ/dt=1.14 uC/s

c)

I=1.14 uC/s

d)

Power supplied to battery

P=EI=(1.14*10-6)*5.83

P=6.65*10-6 =6.65 uW
e)

Power delivered to the resistor is

P=I2R=(1.14*10-6)2*(1.88*106)

P=2.4468 uW

f)

P=VI=(Q/C)I =(4.83/1.31)(1.14)=4.2 uW

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