AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper

The expression for the magnetic field at center of a circular
coil of n turns
B=‌

µ0i

2r

n
If length of the wire is doubled,
2(2πrn)=2πr′n′
(2rn)=‌

r

3

n′
n′=6n
For the same field at the centre,
‌

µ0in

2r

=‌

µ0in′

2r′

‌

µ0in

2r

=‌

µ0i(6n)

2( r 3 )

i′=‌

i

18

Volume will remains same after doubling the length of the coil.
l×A=2l×A′
A=‌

A

2

The resistance after doubling the length,
R′=‌

ρl′

A′

R′=‌

ρ(2l)

( A 2 )

R′=‌

4ρl

A

R′=4R
The emf is,
E′=i′R′
E′=(‌

i

18

)(4R)
E′=‌

2

9

E