Question

An ideal choke draws a current of $8A$ when connected to an $AC$ supply of $100 \, V, 50 \, Hz$. A pure resistor draws a current of 10 A when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the $AC$ source of $150 \, V, 40 \, Hz$. The current in the circuit becomes..........

• A. 18A
• B. 10A
• C. $\frac {15}{{\sqrt {2}}A} $
• D. 8 A

Answer 1

Answer: (C)

Resistance, $R=\frac{100}{10}=10\, \Omega$
Inductive reactance, $X_{L}=2 \pi f L$
$\frac{100}{8} =2 \pi \times 50 \times L$
$\Rightarrow L =\frac{1}{8 \pi} H$
$X_{L}'=2 \pi f' L=2 \pi \times 40 \times \frac{1}{8 \pi}=10\, \Omega$
Impedance of the circuit is
$Z=\sqrt{R^{2}+X_{L}' 2}$
$=\sqrt{(10)^{2}+(10)^{2}}=10 \sqrt{2} \Omega$
Current in the circuit is
$i=\frac{V}{Z}=\frac{150}{10 \sqrt{2}}=\frac{15}{\sqrt{2}} A$