Question

An RL circuit has an emf of $5volts$ , a resistance of $50ohms$ , an inductance of $1henry$ , and no initial current. Find the current in the circuit at any time $t$.

• A. $\frac{1}{20}$
• B. $\frac{1}{50}$
• C. $\frac{1}{10}$
• D. $\frac{1}{40}$

Answer 1

Answer: (C)

$\frac{1}{10}$

Let $I$ be current at ant time $t$

EMF $E=5$ volts , resistance $R=50$ ohms and inductance $L=1$ henry

The basic equation of current for $RL$ circuit is $\frac{dI}{dt}+\frac{R}{L}I=\frac{E}{L}$

$\Rightarrow \frac{dI}{dt}+50I=5$

This is a linear equation and the solution of it is $I=c{e}^{-50t}+\frac{1}{10}$

At $t=0$ , $I=0$. So we get $c=-\frac{1}{10}$

Therefore the equation for current will become $I=-\frac{1}{10}{e}^{-50t}+\frac{1}{10}$

As $t$ tends to infinite , the value of $I$ tends to $\frac{1}{10}$

Therefore the correct option is $C$