First slide

Time -Varying current in L-R circuit

Question

In the circuit shown, switch S is closed at time t = 0. The charge which passes through the battery in one time constant is

Moderate

A

$\frac{{eR}^{2} E}{L}$
B

$E (\frac{L}{R})$
C

$\frac{EL}{{eR}^{2}}$
D

$\frac{eL}{ER}$

Solution

The current at time t is given by
$i = i_{0} (1 - e^{- t / τ})$
$Where i_{0} = \frac{E}{R} and τ = \frac{L}{R}$
$So dQ = idt = i_{0} (1 - e^{- t / τ}) dt$
$Q = \int dQ = \int_{0}^{τ} i_{0} (1 - e^{t / τ}) dt = i_{0} \{[\int_{0}^{τ} dt - \int_{0}^{τ} e^{- t / τ} dt]\}$
$\Rightarrow Q = \frac{\frac{E}{R} \cdot \frac{L}{R}}{e} = \frac{EL}{{eR}^{2}} \Rightarrow Q = \frac{EL}{{eR}^{2}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App