রোধ

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?

হানি নাটস

Inductive reactance = w×Lw\times L

= 0.05×1000Ω0.05\times 1000 \Omega

= 50Ω50 \Omega

Capicitive reactance = 1w×C\dfrac{1}{w\times C}

= 11000×2×10−6\dfrac{1}{1000\times2\times10^-6}

= 500Ω500 \Omega

Source frequency so that the two reactance become equal in magnitude

⇒wL=1wC\Rightarrow w L = \dfrac{1}{wC}

⇒w2=1LC\Rightarrow w^2 = \dfrac{1}{LC}

⇒w=1LC \Rightarrow w =\dfrac{1}{\sqrt {LC}}

=12×10−6×0.05\dfrac{1}{\sqrt{ 2\times10^-6\times0.05}}

=1000101000\sqrt{10} Hz

Then the impedance of circuit becomes equal to resistance

⇒\Rightarrow Impedance of circuit = 100 Ω \Omega

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