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A coil has an inductance of 0.7 H and is...

A coil has an inductance of 0.7 H and is joined in series with a resistance of 220 ohm. Find the wattless component of current in the circuit, when an alternating e.m.f. of 220 V at a frequency of 50 Hz is supplied to it.

Text Solution

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Here, `L = 0.7 H, R = 220 Omega`
`E_(v) = 220 V, v = 50 Hz`
`X_(L) = omega L = 2 pi v L = 2 pi xx 50 xx 0.7 = 220 Omega`
`I_(v) = (E_(v))/(sqrt(R^(Z) + X_(L)^(2))) = (220)/(sqrt(220^(2) + 220^(2))) = (1)/(sqrt2) A`
`tan phi = (X_(L))/(R) = (220)/(220) = 1, phi = 45^(@)`
Wattless component of current `= I_(v) sin phi`
` = (1)/(sqrt2) sin 45^(@) = (1)/(2) = 0.5 A`
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