A series LCR circuit containing 5.0 H inductor, 80µF capacitor and 40 Ω resistor is connected to 230V variable frequency AC source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be – (a). 42 rad/s and 58 rad/s (b). 25 rad/s and 75 rad/s (c). 50 rad/s and 25 rad/s (d). 46 rad/s and 54 rad/s

By BYJU'S Exam Prep

Updated on: September 13th, 2023

We know that

The natural frequency where a medium vibrates at the highest amplitude is the resonance frequency. It is usually denoted as f0. It is witnessed in objects in equilibrium with acting forces and could be vibrating for a long duration under perfect conditions.

The resonance frequency of the LCR series circuit is written as

ω0 = 1/ √LC = 1/√5 x 80 x 10⁻⁶ = 50 rad/s

So half power frequencies are written as

ω = ω0 ± R/2L

Let us substitute the values

ωL = 50 – 40/(2 x 5) = 46 rad/s

ωH = 50 + 40/(2 x 5) = 54 rad/s

Therefore, the angular frequencies of the source at which power is transferred to the circuit are half the power at the resonant angular frequency are likely to be 46 rad/s and 54 rad/s.

Summary: