An RC circuit has a time constant of 2.10 s.At t = 0,the capacitor is fully charged.At what time will the voltage across the capacitor be half of its initial value?
A)0.728 s
B)1.35 s
C)1.46 s
D)1.83 s
E)2.58 s

Question

Quizplus · Accepted Answer

The time constant of an RC circuit is given by the product of resistance and capacitance, τ=RC. In this case, τ=2.10s. 
The voltage across the capacitor as a function of time is given by V(t)=V0(1-e^(-t/τ)), where V0 is the initial voltage across the capacitor. 
We want to find the time at which the voltage across the capacitor is half of its initial value, i.e. V(t)=(1/2)V0. 
Substituting this in the above equation and solving for t, we get t=ln(2)τ=1.46s. Therefore, the correct choice is C.

An RC Circuit Has a Time Constant of 2