Question

An e.m.f. of 15 V is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of currents at time $t=\infty$ and $t=1$ second is

• A. $\frac{e^{1/2}}{e^{1/2}-1}$
• B. $\frac{e^2}{e^2-1}$
• C. $1-\frac{1}{e}$
• D. $\frac{1}{e}$

Answer 1

The correct option is B $\frac{e^2}{e^2-1}$

B. $\frac{e^2}{e^2-1}$

Given, $L=5H$

$R=10\Omega$

$V_0=12V$

The current in $RL$ circuit is,

$I=I_0(1-e^{-t/\tau })$

where $\tau =\frac{L}{R}$

$\tau =\frac{1}{2}sec$

$I_0=\frac{V_0}{R}A$

The current in $LR$ circuit at time $t=\infty sec$,

$I_1=I_0$

The current in $LR$ circuit at time $1sec$

$I_2=I_0(1-e^{-2})$

The ratio of currents at time $t=\infty sec$ and $t=1sec$ is

$\frac{I_1}{I_2}=\frac{I_0}{I_0(1-e^{-2})}$

$\frac{I_1}{I_2}=\frac{e^2}{e^2-1}$