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:
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:
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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.
Updated On: Jun 19, 2026
- 1 : 3
- 3 : 1
- 1 : 9
- 9 : 1
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The Correct Option is B
Solution and Explanation
Step 1: Recall the formula for heat produced.
Heat produced in a conductor due to current: \(H = I^2 R t\), where \(I\) is current, \(R\) resistance, \(t\) time.
Step 2: Set up ratio.
Let currents be \(I_1\) and \(I_2\), resistances equal \(R\). Given: \[ \frac{H_1}{H_2} = \frac{I_1^2 R t}{I_2^2 R t} = \frac{I_1^2}{I_2^2} = 9 \]
Step 3: Solve for current ratio.
\[ \frac{I_1}{I_2} = \sqrt{9} = 3 \]
Step 4: Conclusion.
The ratio of currents is \(I_1 : I_2 = 3 : 1\).
Heat produced in a conductor due to current: \(H = I^2 R t\), where \(I\) is current, \(R\) resistance, \(t\) time.
Step 2: Set up ratio.
Let currents be \(I_1\) and \(I_2\), resistances equal \(R\). Given: \[ \frac{H_1}{H_2} = \frac{I_1^2 R t}{I_2^2 R t} = \frac{I_1^2}{I_2^2} = 9 \]
Step 3: Solve for current ratio.
\[ \frac{I_1}{I_2} = \sqrt{9} = 3 \]
Step 4: Conclusion.
The ratio of currents is \(I_1 : I_2 = 3 : 1\).
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