Single correct option
A series circuit has a resistor , an ideal inductor of reactance and an ideal capacitor of reactance at the supply frequency, connected to a source of rms voltage and variable frequency (the supply is at the frequency where the reactances have the stated values unless told otherwise). Match each quantity in List-I with its value in List-II.
List-I
(P) The rms current in the circuit at the stated frequency
(Q) The average power dissipated at the stated frequency
(R) The rms voltage across the capacitor at the stated frequency
(S) The average power dissipated if the frequency is tuned to resonance (source voltage unchanged)
List-II
(1)
(2) about
(3)
(4)
(5)
List-I
(P) The rms current in the circuit at the stated frequency
(Q) The average power dissipated at the stated frequency
(R) The rms voltage across the capacitor at the stated frequency
(S) The average power dissipated if the frequency is tuned to resonance (source voltage unchanged)
List-II
(1)
(2) about
(3)
(4)
(5)
- A. P→3, Q→4, R→1, S→2
- B. P→3, Q→4, R→5, S→2
- C. P→1, Q→4, R→3, S→2
- D. P→3, Q→2, R→1, S→4
Show answer and solution
Answer: (A) P→3, Q→4, R→1, S→2
At the stated frequency the net reactance is , so the impedance is . The rms current is , so (P) matches 3. The average power is dissipated only in the resistor: , so (Q) matches 4 (equivalently ). The capacitor voltage is , so (R) matches 1; note is the inductor voltage, a distractor. At resonance , , the current becomes and the power is , so (S) matches 2. Therefore P3, Q4, R1, S2.
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