Question

The self inductance of a choke coil is $10mH$. When it is connected with a $10V$ DC source, then the loss of power is $20W$. When it is connected with $10VAC$ source loss of power is $10W$. The frequency of $AC$ source will be

• A. $80Hz$
• B. $100Hz$
• C. $120Hz$
• D. $220Hz$

Answer 1

Answer: (A)

$80Hz$

With $DC$, power $P=\frac{V^2}{R}$
$R=\frac{(10{)}^2}{20}=5\Omega$
with $AC$ power, $P=\frac{V_{rms}^{2}R}{Z^2}$
$Z^2=\frac{(10{)}^2\times 5}{10}=50\Omega$
The impedance, $Z^2=R^2+4{\pi }^2{v}^2{L}^2$
$50=(5{)}^2+(3.14{)}^2\times v^2\times (10\times {10}^{-3}{)}^2$
$v=80Hz$.