A circuit with an electrical load having impedance Z is connected with an AC source as shown in the diagram. The source voltage varies in time as V(t)=300sin(400t)V, where t is time in s. List-I shows various options for the load. The possible currents i(t) in the circuit as a function of time are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II.
List-I
(P) (see structure) (Q) (see structure) (R) (see structure) (S) (see structure)
List-II
(1) (see structure) (2) (see structure) (3) (see structure) (4) (see structure) (5) (see structure)PQRS12345
(A)P→3, Q→5, R→2, S→1✓ Correct
(B)P→1, Q→5, R→2, S→3
(C)P→3, Q→4, R→2, S→1
(D)P→1, Q→4, R→2, S→5
Answer: (A)
Solution
Given: V(t)=300sin(400t) V, so V0=300 V, ω=400 rad/s.
(P) Pure resistor R=30Ω: i=RV=10sin(400t) A, in phase → (3)
(Q)R=30Ω, L=100 mH:
XL=ωL=400×0.1=40Ω
Z=302+402=50Ω
i=6sin(400t−53°) A (current lags) → (5)
(R)R=30Ω, L=25 mH, C=50μF:
XL=400×0.025=10Ω
XC=400×50106=50Ω
Z=302+(50−10)2=50Ω
i=6sin(400t+53°) A (current leads) → (2)
(S)R=60Ω, L=125 mH, C=50μF:
XL=400×0.125=50Ω
XC=50Ω
Resonance: Z=R=60Ω
i=5sin(400t) A, in phase → (1)
Therefore: P→3, Q→5, R→2, S→1
JEE Advanced · 2025 · 18 May 2025 · Paper 1 · Single correct option