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Q.

When an ac source of emf e = E0 sin(100 t) is connected across a circuit, the phase difference between emf e and current i in the circuit is observed to be p/4 as shown in Fig. If the circuit consists possibly only of R-C or L-C or L-R series, find the relationship between the two elements.

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a

R = 1kW, C = 10 mF

b

R = 1 kW, C = 1 mF

c

R = 1 kW, L = 10 H

d

R =1 kW, L = 1 H

answer is A.

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Detailed Solution

Fig. shows that current i leads the emf e by a phase angle π/4. Therefore, the circuit can be R-C circuit alone.tanϕ=XCR=1ωCR=tanπ4=1. e=E0sin100t,ω=100rad/s∴CR=1ω=1100, R=1KΩ=103ΩSolving C=1ωR=10μF
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