Question

A self inductance coil has a resistance of $31.4\Omega$ and a self inductance of $17mH$. The frequency of ac at which the impedance is double the resistance is:

• A. $5000Hz$
• B. $500Hz$
• C. $50Hz$
• D. $250Hz$

Answer 1

The correct option is B $500Hz$

$Z=2R$ (As per question)

$\sqrt{R^2+(\omega L{)}^2}=2R$

$(\omega L{)}^2=3R^2$

$\therefore \omega =\sqrt{\frac{3R^2}{L^2}}$

$=\sqrt{\frac{3\times (31.4{)}^2}{(17\times {10}^{-3}{)}^2}}$

$2\pi f=\sqrt{3}\times \frac{31.4}{10\times {10}^{-3}}$

$\therefore f=\frac{\sqrt{3}\times 31.4}{17\times {10}^{-3}\times 2\times \pi }$

$=509Hz$ (approx)