Question

How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value?

• A. $t_{1/2}=6.93\tau$
• B. $t_{1/2}=69.3\tau$
• C. $t_{1/2}=0.693\tau$
• D. $t_{1/2}=693\tau$

Answer 1

The correct option is C $t_{1/2}=0.693\tau$

For LC circuit, the current at time t is given by , $I=I_0{e}^{-t/\tau }$ where $\tau =RC$, time constant.

When $I=I_0/2,t=t_{1/2}\Rightarrow e^{t_{1/2}/\tau }=2$

Take ln , $t_{1/2}/\tau =ln2$ or $t_{1/2}=0.693\tau$