Question

When $100voltDC$ is applied across a solenoid, a current of $1.0amp$ flows in it. When $100voltAC$ is applied across the same coil, the current drops to $0.5amp.$ If the frequency of the AC source is $50Hz$ 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 $0.55H$

We know that

$i=\frac{V}{R},forDC\Rightarrow R=\frac{100}{1}=100\Omega i=\frac{V}{L\omega },whenACisapplied\Rightarrow L\omega =\frac{V}{i}=\frac{100}{0.5}=200\Omega L=\frac{200}{2\pi \times 50}=0.055H$