Question

When a $100\text{V DC}$ is applied across a solenoid, a current of 1.0 A flows in it. When a $100\text{V AC}$ is applied across the same coil, the current drops to $0.5\text{A}$. If the frequency of the $AC$ source is $50\text{Hz}$, the impedance and inductance of the solenoid are

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

Answer 1

The correct option is A $200\Omega$ and $0.55H$

From given, $Z=\frac{V_{rms}}{I_{rms}}=\frac{100V}{0.5A}=200\Omega$
Now from DC circuit,
$R=\frac{100V}{1A}=100\Omega$
For detailed solution watch the next video
Now in AC circuit
$Z=\sqrt{R^2+X_L^2};X_L=2\pi fL$
$Z=\sqrt{(100{)}^2+(2\pi \times 50\times L{)}^2}$
$\begin{array}{cc}(200{)}^2=& (2\pi \times 50\times L{)}^2+(100{)}^2\\ L& =0.55H\end{array}$