Question

A coil has a resistance of 10 Ω and an inductance of 0.4 henry. It is connected to an AC source of 6.5 V, `30/pi Hz`. Find the average power consumed in the circuit.

Answer 1

Given:
Resistance of coil, R = 10 Ω
Inductance of coil, L = 0.4 Henry
Voltage of AC source, Erms = 6.5 V
Frequency of AC source, `f = 30/pi Hz`
Reactance of resistance-inductance circuit (Z) is given by,
`Z = sqrt(R^2 + X_L^2`
Here, R = resistance of the circuit
           X_L = Reactance of the pure inductive circuit
`Z = sqrt(R^2 + (2pifL)^2`
Average power consumed in the circuit (P) is given by,
`P = E_{rms}l_{rms}cosØ`

`therefore P = 6.5 xx 6.5/Z xx R/Z`

⇒ P = `(6.5xx6.5xx10)/((sqrt(R^2 +(omegaL)^2))`

⇒ P =` (6.5xx6.5xx10)/(100 + 576)`

⇒ `P= (6.5xx6.5xx10)/(676)`

⇒ `P = 0.625 = 5/8 W`