Two heaters are marked 200V, 300W and 200V, 600W. If the heaters are connected in series and the combination connected to a 200V dc supply, then which option is true out of the following ?

Question

Accepted Answer

To understand why Option 3 is the correct answer, we need to analyze the situation where two heaters are connected in series and powered by a 200V DC supply. The heaters are rated at 200V, 300W and 200V, 600W, respectively.

1. **Explanation for Option 3 (Correct Answer): Heat produced in 300W heater is more**

When two resistors (or heaters, in this case) are connected in series, they share the same current. The power dissipated by a resistor in terms of current and resistance is given by the formula $ P = I^2R $. Since both heaters are connected in series, they have the same current flowing through them. The resistance of each heater can be calculated using the formula $ R = \frac{V^2}{P} $.

- For the 300W heater: $ R_1 = \frac{200^2}{300} = \frac{40000}{300} \approx 133.33 \, \Omega $
   - For the 600W heater: $ R_2 = \frac{200^2}{600} = \frac{40000}{600} \approx 66.67 \, \Omega $

Since the current is the same through both heaters, the heater with the higher resistance (300W heater) will dissipate more power in the form of heat. This is because $ P = I^2R $ implies that power is directly proportional to resistance when current is constant. Therefore, the 300W heater, having a higher resistance, will produce more heat.

2. **Explanation for why other options are incorrect:**

- **Option 1: Both the heater will produce same heat**

This option is incorrect because, as explained above, the power dissipated in a resistor in series is dependent on its resistance. Since the resistances are different, the heat produced will not be the same.

- **Option 2: Heat produced in 600W heater is more**

This option is incorrect because the 600W heater has a lower resistance compared to the 300W heater. With the same current flowing through both, the heater with the higher resistance (300W heater) will produce more heat.

- **Option 4: None of these**

This option is incorrect because we have already established that the 300W heater produces more heat than the 600W heater, making Option 3 the correct choice.

In conclusion, the correct answer is Option 3: Heat produced in the 300W heater is more, due to its higher resistance when both heaters are connected in series.