Combination of Resistors: Practice Problem & Solution
The masses of the wires of copper is in the ratio of $1 : 3 : 5$ and their lengths are in the ratio of $5 : 3 : 1$. The ratio of their electrical resistance is: (1988)
Solution Explained:
To solve this problem, we apply the core principles of Combination of Resistors. Understanding the underlying formula is key to arriving at the correct answer below:
Resistance $R = \rho \frac{L}{A} = \frac{\rho d L^2}{m} \propto \frac{L^2}{m}$.
$R_1 : R_2 : R_3 = \frac{5^2}{1} : \frac{3^2}{3} : \frac{1^2}{5} = 25 : 3 : 0.2 = 125 : 15 : 1$.
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