Question

A circular coil of resistance 'R', area 'A', number of turns 'N' is rotated about its vertical diameter with angular speed 'ω' in a uniform magnetic field of induction 'B'. The average power dissipated in a complete cycle is ______.

Options

• `("NAB"omega)/"R"`

• `("N"^2"A"^2"B"^2omega^2)/"2R"`

• `("N"^2"A"^2"B"^2omega^2)/"R"`

• `("NAB"omega)/"2R"`

Answer 1

A circular coil of resistance 'R', area 'A', number of turns 'N' is rotated about its vertical diameter with angular speed 'ω' in a uniform magnetic field of induction 'B'. The average power dissipated in a complete cycle is `underline(("N"^2"A"^2"B"^2omega^2)/"2R")`.

Explanation:

We know e₀ = N A B ω

`therefore "i"_0 ("NAB"omega)/"R"`

Average power dissipated per cycle = `1/2"e"_0"i"_0`

`= 1/2 "N A B"omega xx ("NAB"omega)/"R"`

`= 1/2 ("N"^2"A"^2"B"^2omega)/"R"`