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In an AC circuit driven at angular frequency omega = 50 rad/s, containing ideal inductor(s) and capacitor(s) along with a 100 ohm resistor and a 50 ohm resistor, analysis gives the steady-state voltages and current. Which of the following statement(s) about this circuit is/are correct?

1. The voltage across the 100 ohm resistor = 20*sqrt(2) V.
2. The voltage across the 50 ohm resistor = 20*sqrt(2) V.
3. The current through the circuit I = 2/sqrt(10) A.
4. Both the statement that the voltage across the 100 ohm resistor is 20*sqrt(2) V and that the current is 2/sqrt(10) A are correct.

Correct answer: Both the statement that the voltage across the 100 ohm resistor is 20*sqrt(2) V and that the current is 2/sqrt(10) A are correct.

Solution

This corresponds to the JEE Advanced multi-correct AC problem. Working out the impedances at omega = 50 rad/s and the branch/total currents gives the voltage across the 100 ohm resistor as 20*sqrt(2) V and the line current I = 2/sqrt(10) A. Both of these are the correct statements (the official answer is the combination of these two), while the 50 ohm voltage value and the 1.2 A current are not consistent with the analysis.

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