Question

An ideal choke takes a current of 8A when connected to an a.c source of 100 volt and 50 Hz. A pure resistance under the same conditions takes a current of 10A. If two are connected in series to an a.c. Supply of 150V and 40 Hz, then the current in the series combination of above resistor and conductor is:

Answer 1

$X_L=2\pi fL$

$\frac{100}{8}=2\pi \times 50\times L$

$L=\frac{1}{8\pi }+1$

$X_L=2\pi fL$

$\frac{100}{8}=2\pi \times 50\times L$

$L=\frac{1}{8\pi }+1$

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

The inductive resistance $\Omega$ the choke

$X_L=2\pi fL$

$=2\pi \times 40\times \frac{1}{8\pi }\times 10\Omega$

The impedence in the circuit –

$Z=\sqrt{R^2+X_L^2}$

$=\sqrt{{10}^2+{10}^2}$

$=10\sqrt{2}$

$I=\frac{V}{Z}$ $=\frac{150}{10\sqrt{2}}$ $=\frac{15}{\sqrt{2}}A$