Question

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

• A. 1 : 2
• B. 4 : 1
• C. 1 : 4
• D. 2 : 1

Hint:

The heat produced in a resistor depends on the square of the voltage and inversely on the resistance. Parallel and series connections affect the total resistance and hence the power.

Answer 1

The Correct Option is B

The power dissipated in a resistor is given by the formula: \[ P = \frac{V^2}{R} \] For two identical resistors, the heat produced in parallel and series configurations is as follows:
For parallel connection, the effective resistance is \( R_{\text{eff}} = \frac{R}{2} \), and the power is: \[ P_{\text{parallel}} = \frac{V^2}{R/2} = 2 \frac{V^2}{R} \] For series connection, the effective resistance is \( R_{\text{eff}} = 2R \), and the power is: \[ P_{\text{series}} = \frac{V^2}{2R} \] Now, the ratio of heat produced in parallel to series is: \[ \frac{P_{\text{parallel}}}{P_{\text{series}}} = \frac{2 \frac{V^2}{R}}{\frac{V^2}{2R}} = 4 \] Thus, the ratio of heat produced is \( 4 : 1 \).