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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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The correct Answer is:
`0.5`
`X_L = 2pi vL = 2 xx(22//7) xx50 xx0.7 = 200 Omega`
`Z=sqrt(R^2+X_L^2)=sqrt((220)^2+(220)^2)Omega=220sqrt2Omega`
`I_0=E_0/Z=-(220V)/(220sqrt2Omega)=1/sqrt2A`
Wattless component = `I_0sinphi=(1/sqrt2A)sin45^@=0.5 A`
(as `tanphi =X_L/R =220/220=1` or `phi = 45^@` )
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