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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Correct answer
(MTA)
Solution
In a series circuit with a resistor and a coil (having resistance and inductance ), the phasor relationship for the source voltage is:
Where and , with for an inductive coil.
The magnitude of the source voltage is given by:
Since , the plausible values must satisfy .
Given , then .
Checking the options:
(A) . (Possible, but implies , a purely resistive coil)
(B) . (Possible, but implies , a purely resistive coil)
(C) . (Impossible for a passive RL circuit)
(D) . (Possible, implies , an ideal inductive coil)Option (D) is the most plausible as it represents a standard ideal inductive coil and fits the Pythagorean triple .
Where and , with for an inductive coil.
The magnitude of the source voltage is given by:
Since , the plausible values must satisfy .
Given , then .
Checking the options:
(A) . (Possible, but implies , a purely resistive coil)
(B) . (Possible, but implies , a purely resistive coil)
(C) . (Impossible for a passive RL circuit)
(D) . (Possible, implies , an ideal inductive coil)Option (D) is the most plausible as it represents a standard ideal inductive coil and fits the Pythagorean triple .
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