A circuit with an electrical load having impedance ... is connected with an AC source as shown in the diagram. The source voltage varies in time as , where is time in seconds. List-I shows various options for the load. The possible currents in the circu

Question

A circuit with an electrical load having impedance ... is connected with an AC source as shown in the diagram. The source voltage varies in time as $V (t) = 300 \sin (400 t) V$ , 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. [2025]

Choose the option that describes the correct match between the entries in List-I and those in List-II.

Smart Achievers · Accepted Answer

(1)

$Given V (t) = 300 \sin (400 t)$

$i_{0} = \frac{300}{30} = 10 A, ϕ = 0$

$So, (P) \to (3)$

$Z = \sqrt{R^{2} + {(ω L)}^{2}}$

$= \sqrt{30^{2} + {(400 \times 100 \times 10^{- 3})}^{2}} = 50 Ω$

$∴$ $i_{0} = \frac{300}{50} = 6 A$

and $ϕ = \tan^{- 1} (\frac{ω L}{R}) = 53 °$

i.e., the current lags by $53 °$

$So, (Q) \to (5)$

(R) $Z = \sqrt{{(30)}^{2} + {(\frac{1}{400 \times 500 \times 10^{- 6}} - 400 \times 25 \times 10^{- 3})}^{2}}$

$= \sqrt{30^{2} + 40^{2}} = 50 Ω$

$So, (R) \to (2)$

(S) $Z = \sqrt{60^{2} + {(\frac{1}{50 \times 10^{- 6} \times 400} - 125 \times 10^{- 3} \times 400)}^{2}}$

$= \sqrt{60^{2} + {(50 - 50)}^{2}} = 60 Ω$

$∴$ $i_{0} = \frac{300}{60} = 5 A$

$So, (S) \to (1)$

Solution

1 (P) → (3), (Q) → (5), (R) → (2), (S) → (1)

2 (P) → (1), (Q) → (5), (R) → (2), (S) → (3)

3 (P) → (3), (Q) → (4), (R) → (2), (S) → (1)

4 (P) → (1), (Q) → (4), (R) → (2), (S) → (5)

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