Question

An electric current is passed through a circuit containing two wires of same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 3:2 and 2:3, then the ratio of the current passing through the wire will be
a) 2:3
b) 3:2
c) 8:27
d)27:8​

Answer 1

Given info : An electric current is passed through a circuit containing two wires of same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 3 : 2 and 2 : 3.

To find : the ratio of the current passing through the wire will be ...

solution : we know, resistance of a wire, R = ρl/A

ρ is resistivity and it remains same for the same material.

so, R ∝ l/A

⇒ R ∝ l/πr² [ ∵ A = πr² ]

so, $\frac{R_1}{R_2}=\frac{l_1A_2}{l_2A_1}=\frac{l_1}{l_2}\times\frac{r_2^2}{r_1^2}$ = (3/2)(3/2)² = 27/8

as wires are connected in parallel combination, the potential difference across will be same.

so, potential across the first wire = potential across the 2nd wire

⇒ $i_1R_1=i_2R_2$

⇒ $\frac{i_1}{i_2}=\frac{R_2}{R_1}=\frac{8}{27}$

therefore the ratio of the current passing through the wire will be 8 : 27. hence the correct option is (c).