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For an LCR series circuit with an ac source of angular frequency ω

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a
circuit will be capacitive if ω>1LC
b
circuit will be inductive if ω=1LC
c
power factor of circuit will be unity if capacitive reactance equals inductive reactance
d
current will be leading voltage if ω>1LC

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detailed solution

Correct option is C

The circuit will have inductive nature ifω>1LCωL>1LCHence (1) is false. Also, if circuit has inductive nature, the current will lag behind voltage. Hence (4) is also falseIf ω=1LCωL=1ωC, the circuit will have resistance nature. Hence, (2) is false.Power factor, cosϕ=RR2+ωL-1ωC2=1If ωL=1ωC.Hence, (3) is true.

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