Question

An ideal choke draws a current of $8A$ when connected to an $AC$ supply of $100V,50Hz$. 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 $150V,40Hz$. 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, $X_L=2\pi fL$
$\frac{100}{8}=2\pi \times 50\times L$
$\Rightarrow L=\frac{1}{8\pi }H$
$X_L^{\prime }=2\pi f^{\prime }L=2\pi \times 40\times \frac{1}{8\pi }=10\Omega$
Impedance of the circuit is
$Z=\sqrt{R^2+X_L^{\prime }2}$
$=\sqrt{(10{)}^2+(10{)}^2}=10\sqrt{2}\Omega$
Current in the circuit is
$i=\frac{V}{Z}=\frac{150}{10\sqrt{2}}=\frac{15}{\sqrt{2}}A$