Question

Which of the following wires, all made of the same material, has the highest resistance?

• A. l = 100cm, r = 0.1 cm
• B. l = 200cm, r = 0.2 cm
• C. l = 300cm, r = 0.3 cm
• D. l = 400cm, r = 0.4 cm

Answer 1

The correct option is A l = 100cm, r = 0.1 cm

Resistance of the wire $R=\frac{\rho L}{A}$ where $A=\pi r^2$

$⟹$ $R=k\frac{L}{r^2}$ $(k=\frac{\rho }{\pi }=$constant)

$\therefore$ $R_A=k\frac{100}{(0.1{)}^2}=10000$ $k$

Similarly, $R_B=5000$ $k$ $R_C=3333.3$ $k$ $R_D=2500$ $k$

Hence wire in option A has the highest resistance.