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Question
A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 volt, 50 Hz ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current.
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Solution
R = 1 Ω, L = 0.01 H, V = 200 V, v = 50 Hz.
Impedance of the circuit
`Z = sqrt(R^2 + X_L^2) = sqrt(R^2 + (2pivL)^2)`
= `sqrt((1)^2 + (2 xx 3.14 xx 50 xx 0.1)^2)`
= `sqrt(1 + 9.86) = sqrt(10.86)`
= 3.3 Ω
∴ For phase angle, tan `phi = Z/R`
`tan phi = X_L/R = (2pivL)/R = (2 xx 3.14 xx 50 xx 0.01)/1`
`tan phi` = 3.14
`phi` = tan–1 3.14 = 72°
Phase difference
`phi = (72 xx pi)/180^circ` rad
`phi` = 1.20 radian
Time lag between alternating voltage and current
| `phi` = ωt |
`t = phi/ω = (72 xx pi)/(180 xx 2 xx pi xx 50) = 1/250` sec
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