Question

Currents flowing through two conductors of equal resistance produce 9 times more heat in the first conductor compared to the second one. The ratio of currents flowing through the first and second conductors is:

• A. 1 : 3
• B. 3 : 1
• C. 1 : 9
• D. 9 : 1

Hint:

For equal resistances, the heat produced in conductors is proportional to the square of the current: \(H \propto I^2\). Use this to relate currents when heat ratios are given.

Answer 1

The Correct Option is B

Step 1: Joule heating law.
Heat produced H = I² R t.

Step 2: Setting up the ratio.
H₁/H₂ = (I₁² R t)/(I₂² R t) = I₁²/I₂² = 9.

Step 3: Extracting current ratio.
I₁/I₂ = √9 = 3.

Step 4: Conclusion.
The currents are in the ratio 3:1.