$A$ 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 $V(t) = 300 \sin (400 t) \text{ V}$,where $t$ is time in seconds. 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-$I$ List-$II$
$(P)$ Resistor $R = 30 \ \Omega$ $(1)$ $i(t) = 5 \sin(400t)$
$(Q)$ Resistor $R = 30 \ \Omega$ and Inductor $L = 100 \text{ mH}$ $(2)$ $i(t) = 6 \sin(400t + 53^{\circ})$
$(R)$ Capacitor $C = 50 \ \mu\text{F}$,Resistor $R = 30 \ \Omega$,and Inductor $L = 25 \text{ mH}$ $(3)$ $i(t) = 10 \sin(400t)$
$(S)$ Capacitor $C = 50 \ \mu\text{F}$,Resistor $R = 60 \ \Omega$,and Inductor $L = 125 \text{ mH}$ $(4)$ $i(t) = 20 \sin(400t - 90^{\circ})$
$(5)$ $i(t) = 6 \sin(400t - 53^{\circ})$

  • A
    $P \rightarrow 3, Q \rightarrow 4, R \rightarrow 2, S \rightarrow 1$
  • B
    $P \rightarrow 1, Q \rightarrow 5, R \rightarrow 2, S \rightarrow 3$
  • C
    $P \rightarrow 3, Q \rightarrow 5, R \rightarrow 2, S \rightarrow 1$
  • D
    $P \rightarrow 1, Q \rightarrow 4, R \rightarrow 2, S \rightarrow 5$

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