Answer MET Question 14

Question: A. What is meant by “Resonance” in RLC circuits? Compare the series and parallel resonance circuits.

Answer: Resonance in the RLC circuit is the condition when reactances of capacitor and inductor coil are equal in magnitude.

Capacitors and Inductors are both components which can store energy: capacitors store it in an electric field and inductors in a magnetic field.

Ideal capacitors and inductors are assumed to have zero resistance and so have a purely imaginary impedance,

ZC=1jωC=−jωC and ZL=jωL

and their reactances to be, XC=−1/ωC and XL=ωL

Series Resonance Circuit	Parallel Resonance Circuit
A series resonance circuit has a capability to draw heavy currents and power from the mains. So it is regarded as an acceptor circuit.	A parallel resonance circuit has a capability to very small currents and power from the mains. So it is regarded as a rejector circuit.
Current at resonance is maximum and given by V/R	Current at resonance is minimum and given by VCR/L
Resonant frequency  = $\displaystyle \small \mathrm{\frac{1}{2\pi \sqrt{LC}}}$	Resonant frequency = $\displaystyle \small \mathrm{\frac{1}{2\pi \sqrt{\frac{1}{LC}-\left ( \frac{R}{L} \right )^2}}}$
Power factor is unity	Power factor is unity
Effective impedance is minimum and given by R	Effective impedance is maximum = $\displaystyle \small \mathrm{\frac{L}{CR}}$