Question

Two wires A and B of same material and same mass have radius $2$r and r. If resistance of wire A is $34\Omega$, then resistance of B will be?

• A. $544\Omega$
• B. $272\Omega$
• C. $68\Omega$
• D. $17\Omega$

Answer 1

The correct option is A $544\Omega$

The radius has a ratio of $2:1$, therefore the cross-sectional area is of ratio $4:1.$

The resistance per unit length is therefore $1:4.$

Because we are told the mass is the same, wire $B$, the smaller section wire will have to be $4$ times as long to have the same mass, neglecting the effects of any insulation on the mass.

So the final resistance of $B$ will be $16$ times the resistance of $A$ or $544$ Ohms.