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Question

A circuit connected to an ac source of emf e=e0sin(100t) with t in seconds, gives a phase difference of π4 between the emf e and current i. Which of the following circuits will exhibit this?

A
RL circuit with R=1 kΩ and L=1 mH
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B
RL circuit with R=1 kΩ and L=10 mH
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C
RC circuit with R=1 kΩ and C=10 μF
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D
RC circuit with R=1 kΩ and C=1 μF
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Solution

The correct option is C RC circuit with R=1 kΩ and C=10 μF
No information is given about leading or lagging quantity between emf and current. So, the circuit can be RC or RL.

Now, ω=100 rad/s
As,
tanϕ=XR

Here, X can be either XC or XL

Considering R=1 kΩ, as this value is common to all options.

So, tan45=XRR=X

X=1000 Ω

Now, considering XL=1000 Ω

ωL=1000

100×L=1000 L=10 H

Now, Considering XC=1000 Ω

So, 1ωC=1000

1100×C=1000C=105 F=10 μF

So, the phase difference between emf and current will be 45 if

R=1 kΩ, L=10 H or
R=1 kΩ, C=10 μF

Hence, (D) is the correct answer.

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