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A circular coil of radius 8.0cm and 20 t...

A circular coil of radius 8.0cm and 20 turns rotated about its vertical diameter with an angular speed of `50"rads"^(-1)` uniform horizontal magnetic field of magnitude `3xx10^(-2)T.` Obtain the maximum and average emf induced in the coil if the coil froms a closed loop of resistance `10Omega` then calculate the average power loss due to joule heating.

Text Solution

Verified by Experts

Given :
Radius of coil, `r=8.0cm`
`=8xx10^(-2)m`
N = 20 turns, `omega=50"rad"^(-1)`
To find : `B=3xx10^(-2)T,em=?e=?`
Resistance `R=10W,"Power"P=?`
We know, `e_(m)=NBAW`
`=N(pir^(2))Bomega`
`e_(m)=20xx(22)/(7)xx(8xx10^(-2))xx3xx10^(-2)xx5`
`e_(m)=0.6003V`
Average value of emf induced over a full cycle, `e_(m)=0`
`I_(m)=(e_(m))/(R)=(0.603)/(10)=0.0603A`
Average power dissipated, `P_(av)=(e_(m)I_(m))/(2)`
`=(0.603xx0.0603)/(2)`
`P_(av)=0.018W`
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