A series RC circuit consists of a battery,a switch,a resistor,and a capacitor.In terms of the time constant
Of this circuit,how long after the switch is closed does the current in the circuit reach half of its maximum value?
A)0.500
B)1.50
C)0.693
D)2.00

Question

A series RC circuit consists of a battery,a switch,a resistor,and a capacitor.In terms of the time constant 
Of this circuit,how long after the switch is closed does the current in the circuit reach half of its maximum value?
A)0.500 
B)1.50 
C)0.693 
D)2.00

Quizplus · Accepted Answer

The time constant of an RC circuit is given by the product of resistance and capacitance, i.e., tau = RC. At the time when the current in the circuit reaches half of its maximum value, the charge Q on the capacitor is also half of its maximum value. Using the formula for the charge on a capacitor in an RC circuit, Q = Q0(1 - e^(-t/tau)), where Q0 is the maximum charge on the capacitor, we can solve for the time t when Q = Q0/2:

Q/Q0 = 1/2 = 1 - e^(-t/tau)
e^(-t/tau) = 1/2
-t/tau = ln(1/2)
t = tau*ln(2) = 0.693*tau

Therefore, the time taken for the current to reach half of its maximum value is 0.693 times the time constant of the circuit. The best choice is C.

A Series RC Circuit Consists of a Battery,a Switch,a Resistor,and