Question

Two resistances A and B of same length have area of cross-section 0.2 mm² and 0.4 mm². If the resistance of A is 16 Ω. What is the resistance of B?

Answer 1

Given: a_A = 0.2 mm², a_B = 0.4 mm², R_A = 16 Ω

Assuming both conductors have the same material and temperature, their resistivity and length are equal.

Formula: \[R=\rho\frac{l}{A}\]

For equal resistivity and length:

\[\frac{R_B}{R_A}=\frac{a_A}{a_B}\]

\[R_B=R_A\frac{a_A}{a_B}\]

\[=16\Omega\times\frac{0.2\text{mm}^{2}}{0.4\text{mm}^{2}}\]

\[=16\Omega\times\frac{1}{2}\]

= 8 Ω