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A circuit connected to an ac source of emf e = e0 sin (100t) with t in seconds, gives a phase difference of π/4 between the emf and current. Which of the following circuits will exhibit this?
(1) R L circuit with R = 1 kΩ and L = 10 mH
(2) R L circuit with R = 1 kΩ and L = 1 mH
(3) R C circuit with R = 1 kΩ and C = 1 μF
(4) R C circuit with R = 1 kΩ and C = 10 μF
- R L circuit with R = 1 kΩ and L = 10 mH
- R L circuit with R = 1 kΩ and L = 1 mH
- R C circuit with R = 1 kΩ and C = 1 μF
- R C circuit with R = 1 kΩ and C = 10 μF
Correct answer: R C circuit with R = 1 kΩ and C = 10 μF
Solution
Phase difference pi/4 requires reactance = resistance. With w=100 rad/s and R=1 kohm, for an RC circuit 1/(wC)=R gives C = 1/(100*1000) = 10 uF. (RL would need L=10 H, not offered.)
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