AP EAPCET 25-Aug-2021 Shift 1 Paper

Magnetic field due to first coil and second coil is same at centre.
Then, magnetic field al centre is
B=

µ0I1

2(2r)

=

µ0I2

2(r)

⇒

I1

I2

=2 ...(i)
As we know that, resistance of the coil is related as
R=ρ

l

A

where, ρ= resistivity
l= length
A= area of cross-section
ρ and A are same for both coils but
l1=2π(2r) and l2=2π(r)
⇒

l2

l1

=

1

2

...(ii)
If V1 and V2 are potential difference applied across first and second coil, then
I1=

V1

R1

and I2=

V2

R2

I1=

V1

ρ 1 A

...(iii)
and l2=

V2

ρ l2 A

...(iv)
From Eqs. (i), (iii) and (iv), we get

V1

I1

×

I2

V2

=2
⇒

V1

V2

×

l2

l1

=2
⇒

V1

V2

×

1

2

=2 [Form Eq. (ii)]
⇒

V1

V2

=4