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When an inductor coil is connected to an...

When an inductor coil is connected to an ideal battery of emf 10V, a constant current 2.5 A flows. When the same inductor coil is connected to an ac source of 10V and 50 HZ then the current is 2A. Find out the inductance of the coil.

Text Solution

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When the coil is connected to `dc` source the final current is decided by the resistance of the coil. `therefore r=10/2.5=4 Omega`
When the coil is connected to `ac` source, the final current is decided by the impedance of the coil. `therefore Z=10/2=5Omega`
But `Z=sqrt((r)^(2)+(X_(L))^(2)) X_(L)^(2)=5^(2)-4^(2)=9`
`X_(L)=3 Omega`
`therefore omegaL=2pifL=3`
`therefore 2pi50L=3`
`therefore L=3//100pi` Henry
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