Question

In the adjoining circuit, calculate the inductive reactance and the capacitive reactance. What should be the source frequency so that the two reactance become equal in magnitude? What would then be the impedance(in ohms) of the circuit?

Answer 1

Inductive reactance = $w\times L$

= $0.05\times 1000\Omega$

= $50\Omega$

Capicitive reactance = $\frac{1}{w\times C}$

= $\frac{1}{1000\times 2\times {10}^{-}6}$

= $500\Omega$

Source frequency so that the two reactance become equal in magnitude

$\Rightarrow wL=\frac{1}{wC}$

$\Rightarrow w^2=\frac{1}{LC}$

$\Rightarrow w=\frac{1}{\sqrt{LC}}$

=$\frac{1}{\sqrt{2\times {10}^{-}6\times 0.05}}$

=$1000\sqrt{10}$ Hz

Then the impedance of circuit becomes equal to resistance

$\Rightarrow$ Impedance of circuit = 100 $\Omega$