Question

A certain choke coil of negligible resistance draws a current of 8A, when connected to a supply of 100 volts, at 50Hz. A certain non-inductive resistance, under the same conditions carries a current of 10 A. If the two are transferred to a supply system working at 150 V, at 40 Hz, the total current they will take if joined in series is

• A. 1.06 A
• B. 10.6 A
• C. 0.106 A
• D. 100.6 A

Answer 1

Answer: (B)

10.6 A

In choke coil, $I=8A,Erms=100V$

$\omega =100\pi rad/s$

$\frac{100}{100\pi \times L}=8=L=\frac{1}{8\pi }H$

In resistance, $I=10amp$

$\therefore R=\frac{100}{10}=10\Omega$

New source V=150 V, f= 40 Hz, ${\omega }^{\prime }=40\times 2\pi$

Connected in series, $z=\sqrt{{10}^2+\left(\frac{80\pi }{8\pi }\right)}$

$=10\sqrt{2}\Omega$

$Irms=\frac{150}{10\sqrt{2}}$

$=10.61A$