Question

Two resistors are connected in series across a $5\text{V rms}$ source of alternating potential. The potential difference across $6\Omega$ resistor is $3\text{V}$. If R is replaced by a pure inductor $L$ of such magnitude that current remains same, then the potential difference across $L$ is

• A. $1\text{V}$
• B. $2\text{V}$
• C. $3\text{V}$
• D. $4\text{V}$

Answer 1

The correct option is D $4\text{V}$

From given
$V=IR$
$I=\frac{3V}{6\Omega }=0.5A$

$Z=\sqrt{X_L^2+36}$
As
$V=IZ$
$Z=\frac{V}{I}=\frac{5}{0.5}=10\Omega$
Now,
$\sqrt{X_L^2+36}=10$
$X_L^2+36=100$
$X_L=\sqrt{64}=8\Omega$

Therfore potential across inductor,
$V_L=X_{L}I$
$V_L=8\times 0.5$
$V_L=4V$.