Question

A coil of inductance L and resistance r is connected in series with a 4 $\Omega$ resistor to a battery of emf E volt through a switch S. The switch S is closed at time $t=0s$ and the potential dlfference across the inductor $\left(V_{ab}\right)$ is measured and its variation in time t is shown in the above graph. FInd the resistance of the coil (in $\Omega$).

• A. $1\Omega$
• B. $1.2\Omega$
• C. $4\Omega$
• D. $2\Omega$

Answer 1

The correct option is A $1\Omega$

At $t=0$s, due to induction, L behaves as an open circuit, current in the circuit is zero.
$\therefore V_{ab}=E=10V,$ from the graph
After long time, steady current $I_0$ is established, the coil behaves like a resistor of resistance r.
As$t\to \infty ,V_{ab}=2.0=I_{0}r$
Now, Applying KVL
$\therefore E-4I_0-I_{0}r=0$
i.e.$10-4I_0-2=0$
or$I_0=2A$

Now $r=\frac{2}{I_0}=\frac{2}{2}=1\Omega$