Question

two nichrome wire A and B each of length 5 cm and of radius 1 cm and 3 cm respectively are connected to each other in series if a current of 5 ampere flows through the combination of wires the ratio of potential difference across wire a to that across via b will be

Answer 1

we know, resistance is given by $R=\rho\frac{L}{A}$
here, $\rho$ is resistivity of material, L is length of conductor, A is cross section area of conductor.

so, resistance of wire A , $R_A=\rho\frac{5}{\pi(1)^2}$
resistance of wire B, $R_B=\rho\frac{5}{\pi (3)^2}$

both wire are joined in series combination.
so, current through each wire will be same.
now, potential across wire A , $V_A=5\rho\frac{5}{\pi(1)^2}$
potential across wire B, $V_B=5\rho\frac{5}{\pi(3)^2}$

so, ratio of potential across wire A and B
= $\frac{3^2}{1^2}=\frac{9}{1}$

Answer 2

correct answer is 9:1