Question

Two wires A and B, made of same material and having their lengths in the ratio 6 : 1 are connected in series. The potential differences across the wires are 3V and 2V respectively. If r${}_A$ and r${}_B$ the radii of A and B respectively, then $\frac{r_B}{r_A}$ is

• A. 1:4
• B. 1:2
• C. 1:1
• D. 2:1

Answer 1

Answer: (B)

1:2

$\frac{L_1}{L_2}=\frac{6}{1}$

$V_1=3V,V_2=2V$

$V_1=I{R}_1;V_2=I{R}_2$

$\frac{V_1}{V_2}=\frac{R_1}{R_2}$

$\frac{3}{2}=\frac{L_1}{L_2}\left(\frac{A_2}{A_1}\right)$

$\frac{3}{2}=\frac{6}{1}\left(\frac{A_2}{A_1}\right)$

$\frac{A_1}{A_2}=\frac{4}{1}$

$\frac{r_1}{r_2}=\frac{2}{1}$

$\frac{r_2}{r_1}=\frac{1}{2}$