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Q.

An inductance L, a capacitance C and a resistance R may be connected to an ac source of angular frequency $ω$ , in three different combinations of RC, RL and LC in series. Assume that $ωL = \frac{1}{ωC}$ . The power drawn by the three combinations are P₁ , P₂ , P₃ respectively. Then

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a

P₁ = P_{2 >} P₃

b

P₁ = P_{2 <} P₃

c

P₁ > P₂> P₃

d

P₁ = P₂= P₃

answer is B.

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Detailed Solution

In RC circuit p₁= $\frac{E_{0} I_{0}}{2} \cos ϕ$ , Where $\cos ϕ = \frac{R}{Z}$

In RL circuit p₂= $\frac{E_{0} I_{0}}{2} \cos φ$ , Where $\cos ϕ = \frac{R}{Z}$

$ϕ$ is same for both RC and RL circuits , so P₁=P₂

In LC circuit P₃ , As there is no resistor in LC circuit it consumes no power.

Therefore $P_{1} = P_{2} > P_{3}$

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An inductance L, a capacitance C and a resistance R may be connected to an ac source of angular frequency ω , in three different combinations of RC, RL and LC in series. Assume that ωL=1ωC. The power drawn by the three combinations are P1 , P2 , P3 respectively. Then