Answer
a) $R_B=4R_A$
Thus, the resistance of light B is greater than that of light A.
b) $\frac{R_B}{R_A}=4$
Work Step by Step
(a) We know that
$\rho=\frac{V^2}{R}$
As given that
$\rho_A=4\rho_B$
$\implies \frac{V^2}{R_A}=\frac{4v^2}{R_B}$
This can be rearranged as:
$R_B=4R_A$
Thus, the resistance of light B is greater than that of light A.
(b) We know that
$\rho=\frac{V^2}{R}$
As given that
$\rho_A=4\rho_B$
$\implies \frac{V^2}{R_A}=\frac{4v^2}{R_B}$
This can be rearranged as:
$R_B=4R_A$
$\implies \frac{R_B}{R_A}=4$
This is the required ratio.
