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InterviewSolution
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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 acrossR is ___________(a) \(\sqrt{\frac{5}{8}}\) Vrms(b) \(\sqrt{\frac{2}{3}}\) Vrms(c) \(\sqrt{\frac{8}{5}}\) Vrms(d) \(\sqrt{2}\) VrmsThis question was addressed to me in examination.Question is taken from Advanced Problems on Resonance in section Resonance & Magnetically Coupled Circuit of Network Theory |
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Answer» 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. |
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