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

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