A voltage of 12 cos (I000t+45) Vis applied to a circuit in which a resistor of 4. n, aninductor of L H, and a capacitor of 100 μF are connected in series. If the current in the circuit is in phase with the voltage, find the value of L

Question

Darwin Lee

Physics

4 January, 08:32

A voltage of 12 cos (I000t+45) Vis applied to a circuit in which a resistor of 4. n, aninductor of L H, and a capacitor of 100 μF are connected in series. If the current in the circuit is in phase with the voltage, find the value of L

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Answers (1)

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Brennan Frey · Answer 1

0.01 H

Explanation:

V = 12 cos (1000t + 45)

C = 100 micro farad

Let the inductance be L.

When the current and the voltage are in the same phase so it is the condition of resonance.

So capacitive reactance = inductive reactance

Xc = XL

1/ωC = ωL

L = 1 / ω²C

By comparisonV = Vo Cos (ωt + Ф)

ω = 1000 rad/s

L = 1 / (1000 x 1000 x 100 x 10^-6)

L = 1 / 100

L = 0.01H

thus, the inductance of the inductor is 0.01 H.