Question

Two wires of the same material and the same radius have their lengths in the ratio 2 : 3. They are connected in parallel to a battery which supplies a current of 15 A. Find the current through the wires.

Answer 1

Given: The ratio of their lengths is:

R₁ : R₂ = 2 : 3

Total current = 15 A

Resistance of a wire (R) = `rho l/A`

Since they are connected in parallel, the current divides inversely to their resistances.

I₁ : I₂ = `1/R_1 : 1/R_2` = 3 : 2

Let,

I₁ = 3x    ...(i)

I₂ = 2x    ...(ii)

3x + 2x = 15

5x = 15

x = `15/5`

x = 3

By putting the value of x in equation (i), we get,

I₁ = 3x

= 3(3)

= 9 A

By putting the value of x in equation (ii), we get,

I₂ = 2x

= 2(3)

= 6 A