GATE EE 2016 Set 2 — Question 21
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Electric Circuits → Transient & AC Steady-State → Phasors, Impedance & Admittance
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Question
A resistance and a coil are connected in series and supplied from a single phase, , ac source as shown in the figure below. The rms values of plausible voltages across the resistance () and coil () respectively, in volts, are
- A.65, 35
- B.50, 50
- C.60, 90
- D.60, 80
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Solution
Let the coil have resistance and inductance (the dashed box in the figure contains both). The resistor voltage is in phase with the current, while the coil voltage leads the current by an angle , where .From the phasor sum :For a real coil with both and , , so . With :
- (A) 65, 35: , i.e. : the coil would need zero inductance.
- (B) 50, 50: : again a coil with zero inductance.
- (C) 60, 90: : the coil voltage would have to lag the current, which no – coil can do. Impossible.
- (D) 60, 80: , i.e. : a purely inductive coil with zero resistance.
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