Question

Two uniform wires A and B are of the same metal and have equal masses. The radius of wire A is twice that of wire B. The total resistance of A and B when connected in parallel is

• A. $4\Omega$ when the resistance of wire A is $4.25\Omega$
• B. $5\Omega$ when the resistance of wire A is $4\Omega$
• C. $4\Omega$ when the resistance of wire B is $4.25\Omega$
• D. $5\Omega$ when the resistance of wire B is $4\Omega$

Answer 1

The correct option is A $4\Omega$ when the resistance of wire A is $4.25\Omega$

Density and masses of wire are same so their volumes are same i.e. $A_1{l}_1=A_2{l}_2$
Ratio of resistances of wires A and B $\frac{R_A}{R_B}=\frac{l_1}{l_2}\times \frac{A_2}{A_1}={\left(\frac{A_2}{A_1}\right)}^2={\left(\frac{r_2}{r_1}\right)}^4$
Since $r_1=2r_2$ so $\frac{R_A}{R_B}=\frac{1}{16}\Rightarrow R_B=16R_A$
Resistance $R_A$ and $R_B$ are connected in parallel so equivalent resistance $R=\frac{R_A{R}_B}{R_A+R_B}=\frac{16R_A}{17}$, By checking correctness of equivalent resistance from options, only option (a) is correct