Question

Brightness Problems,
31. In the following diagram, the lengths of wires AB and
BC are equal, but the radius of wire AB is double
that of BC. The ratio of potential gradient on wires
AB and on BC will be (wires are made of same
material)
(1) 4:1
(3) 2:1
(2) 1:4
(4) 1:1
​

Answer 1

• The ratio of potential gradient on wires  AB and on BC will be ( if wires are made of same  material) 1 : 4

I assumed a simplest circuit diagram and found the ratio of potential gradient on wires AB and on BC.

It is given that radius of AB is double than that of BC.

Let take the radius of BC be r.

So radius of AB = 2r

And current in the circuit is = i

Here resistivity of wire AB and BC is ρ.

And length of AB = BC = l

So, resistance of wire AB is = ρl/ A

R= ρl/π(2r)² = ρl/4πr²

Then potential difference across wire AB is

V = iR = i ρl/4πr²

Potential gradient on wire AB is

G =V/l = i ρl/4πr² l = iρ/4πr²

Now resistance of wire BC = ρl/πr²

and Potential difference across BC = iρl/πr²

and potential gradient across BC = iρ/πr²

Hence ratio of potential gradient across AB and BC is 1:4.