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Two concentric coplanar circular loops m...

Two concentric coplanar circular loops made of wire with resistance per unit length `10^(-4)Omega//m`, have diameters 0.2 m and 2m. A time varying potential difference (4+2.5t) volt is applied to the larger loop. Calculate the current in the smaller loop.

Text Solution

Verified by Experts

The resistance of the loops
`R_(1)=2pir_(1)xx10=2pixx0.1xx10`
`=6.28 Omega`
and `R_(2)=2pir_(2)=2pixx1xx10`
`=62.8Omega`
Flux in the smaller loop `phi=B_(2)A_(1)`
`=(mu_(0)i2)/(2r_(2))pir_(1)^(2)`
`=(mu_(0)i_(2))/(2r_(2))pir_(1)^(2)`
`=(mu_(0)[V/(R_(2))]pir_(1)^(2))/(2r_(2))`
`=(mu_(0)([4+2.5t])/(R_(2))pir_(1)^(2))/(2r_(2))`
The induced curretn `i_(1)=e/(R_(1))=([d phi //dt])/(R_(1))`
After substituting the value and simplifying we get
`i=1.25 A`
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Knowledge Check

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