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)=300 (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. [figure] Choose the option that describes the correct match between the entries in List-I to those in List-II.
- P → 3, Q → 5, R → 2, S → 1
- P → 1, Q → 5, R → 2, S → 3
- P → 3, Q → 4, R → 2, S → 1
- P → 1, Q → 4, R → 2, S → 5
Answer
(1) P → 3, Q → 5, R → 2, S → 1
Solution
=400 rad s-1, V0=300 V; i0= V0Z, = XL-XCR.
(P) R=30 : i=10 400t, in phase → 3
(Q) XL=400 0.1=40 , Z= 302+402=50 , i0=6 A, current lags by 53 (negative at t=0, peak after 2) → 5
(R) XC= 1400 50 10-6=50 , XL=10 , Z= 302+402=50 , i0=6 A, current leads by 53 (positive at t=0, peak before 2) → 2
(S) XL=400 0.125=50 =XC: resonance, Z=60 , i=5 400t → 1
Answer: (A)