Question

Two wires of resistances \( R_1 \) and \( R_2 \) are connected to a cell in parallel. If the currents flowing in them are \( i_1 \) and \( i_2 \), and the heats produced in them are \( H_1 \) and \( H_2 \), respectively, per second, the ratio of heat is:

• A. \( \frac{H_1}{H_2} = \frac{R_2}{R_1} \).
• B. \( \frac{H_1}{H_2} = \frac{R_1}{R_2} \).
• C. \( \frac{H_1}{H_2} = \frac{i_1^2}{i_2^2} \).
• D. \( \frac{H_1}{H_2} = \frac{i_2}{i_1} \).

Hint:

In a parallel circuit, heat produced is directly proportional to the {resistance} when the voltage is constant. Use Joule’s law \( H = I^2 R t \) for calculations.

Answer 1

The Correct Option is A

According to Joule’s Law of Heating, the heat produced in a conductor is given by \( H = I^2 R t \). Since the resistances are connected in parallel, the potential difference across each resistor is the same. Using the relation between current and resistance in a parallel circuit, we know that \( I = \frac{V}{R} \). Therefore, the heat produced is directly proportional to the resistance when the current is constant. Thus, the ratio of the heats produced in the two wires is: \[ \frac{H_1}{H_2} = \frac{R_2}{R_1} \]