Question

The RL circuit in the below figure is fed from a constant magnitude, variable frequency sinusoidal voltage source VIN. At 50 Hz, the R and L elements each have a voltage drop Vrms. If the frequency of the source is changed to 25 Hz, the new voltage drop across  R is ___________

(a) \(\sqrt{\frac{5}{8}}\) Vrms

(b) \(\sqrt{\frac{2}{3}}\) Vrms

(c) \(\sqrt{\frac{8}{5}}\) Vrms

(d) \(\sqrt{2}\) Vrms

This question was addressed to me in examination.

Question is taken from Advanced Problems on Resonance in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right option is (c) \(\sqrt{\frac{8}{5}}\) Vrms

Easiest explanation: At 50 Hz, VR = VL and R = ωL

Also Vrms = \(\frac{V_{in}}{\sqrt{2}} \)

At 25 Hz, Iin  = \(\frac{V_{in}}{\sqrt{R^2+\frac{ω^2 L^2}{4}}}\)

= \(\frac{V_{in}}{\sqrt{ω^2 L^2 + \frac{ω^2 L^2}{4}}} = \frac{2V_{in}}{\sqrt{5} ωL}\)

So, Vnew = \(\frac{2V_{in}}{\sqrt{5} ωL} × R = \frac{2V_{in}}{\sqrt{5}}\)

=  \(\frac{2\sqrt{2} V_{rms}}{\sqrt{5}} = \sqrt{\frac{8}{5}}\) Vrms.