Question

When $100V$ dc is supplied across a solenoid, a current of $1.0A$ flows in it. When $100V$ ac is applied across the same coil, the current drops to $0.5A$. If the frequency of ac source is $50Hz$, then the impedance and inductance of the solenoid are

• A. $200\Omega \text{and}0.55H$
• B. $100\Omega \text{and}0.86H$
• C. $200\Omega \text{and}1.0H$
• D. $100\Omega \text{and}0.93H$

Answer 1

The correct option is A

$200\Omega \text{and}0.55H$

For dc, $R=\frac{V}{i}=\frac{100}{1}=100\Omega$

For ac, $Z=\frac{V}{i}=\frac{100}{0.5}=200\Omega$

$\because Z=\sqrt{R^2+(\omega L{)}^2}\Rightarrow 200=\sqrt{(100{)}^2+4{\pi }^2(50{)}^2{L}^2}$

$\therefore L=0.55H$