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When an AC source of e.m. f. e=E0sin(100t) is connected across a circuit, the phase difference between the e.m.f. e and the current i in the circuit is observed to be π/4, as shown in the diagram. If the circuit consists possibly only of RC or RL in series, find the relationship between the two elements.

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a

R=1kΩ, C=10 μF

b

R=1kΩ,C=1 μF

c

R=1kΩ, L=10 H

d

R=1kΩ, L=1 H

answer is A.

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Detailed Solution

As the current i leads the voltage by π4, it is an RC circuit, hence, tanϕ=XCR⇒tanπ4=1ωCR ⇒ωCR=1 as ω=100 rad/sec⇒CR=1100 sec−1From all the given options only option (1) is correct.

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When an AC source of e.m. f. e=E0sin(100t) is connected across a circuit, the phase difference between the e.m.f. e and the current i in the circuit is observed to be π/4, as shown in the diagram. If the circuit consists possibly only of RC or RL in series, find the relationship between the two elements.