Answer to Question #155049 in Electricity and Magnetism for Anto abheshek

Question

A resistor of 50 ohm on inductor of 20/π Hendry and a capacitor of 5 /5 micro farate are connected in a series to a voltage source of 230 volt, 50 hz find the inpedence of the circuit

Answer 1

Answer

For given LCR circuit

$X_L=2\pi fL$

$X_L=2\pi\times 50\times\frac{20}{\pi}=2000 ohm$

$X_c=\frac{1}{2\pi fc}=\frac{1}{2\pi \times50\times\frac{5}{\pi}\times10^{-6}}=2000ohm$

Impendence of circuit can be given as

$Z=\sqrt{R^2+(X_L-X_c)^2}\\Z=\sqrt{50^2+(2000-2000)^2}\\Z=50ohm$

So impendence if circuit is 50ohm