A resistance and a coil are connected in series across 100 V rms, 50 Hz. The figure shows the coil’s resistance and inductance. Which rms pair (VR,VC) is plausible, in volts?
**Official disposition: marks to all (MTA).** The source key does not require one particular option.
For the coil modeled as r+jX with X>0, VR is in phase with current while VC leads it by θ between 0° and 90°. They satisfy $100^2=V_R^2+V_C^2+2V_RV_C\cos\theta$.
The pair 60,90 gives cosθ=(10000−3600−8100)/(10800)<0, incompatible with an ordinary passive coil. The pair 60,80 requires θ=90°, corresponding to a lossless coil. The pairs summing to 100 require θ=0°. The nonideal drawing and ambiguous intended idealizations make a unique plausible choice problematic; preserve MTA rather than forcing one.
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