A heater A gives out 300 W of heat when connected to a 200 V d.c supply . A second heater B gives out 600 W when connected to a 200 v.d.c. supply . If a series combination of the two heaters is connected to a 200 V d.c. supply the heat output will be

Options

A. 100 W
B. 450 W
C. 300 V
D. 200 W

Answer

To solve the problem, we need to find the heat output when both heaters A and B are connected in series to a 200 V d.c. supply. We will follow these steps:

### Step 1: Calculate the resistance of heater A
Given that heater A gives out 300 W when connected to a 200 V supply, we can use the power formula:
\[ P = \frac{V^2}{R} \]
Rearranging this gives us:
\[ R_A = \frac{V^2}{P} \]

Substituting the known values:
\[ R_A = \frac{200^2}{300} = \frac{40000}{300} = \frac{400}{3} \, \Omega \]

### Step 2: Calculate the resistance of heater B
Similarly, for heater B, which gives out 600 W at the same voltage:
\[ R_B = \frac{V^2}{P} \]

Substituting the known values:
\[ R_B = \frac{200^2}{600} = \frac{40000}{600} = \frac{200}{3} \, \Omega \]

### Step 3: Calculate the total resistance in series
When the two heaters are connected in series, the total resistance \( R_{total} \) is the sum of the individual resistances:
\[ R_{total} = R_A + R_B \]

Substituting the values we calculated:
\[ R_{total} = \frac{400}{3} + \frac{200}{3} = \frac{600}{3} = 200 \, \Omega \]

### Step 4: Calculate the total power output when both heaters are connected in series
Now, we can calculate the total power output when both heaters are connected in series using the formula:
\[ P_{total} = \frac{V^2}{R_{total}} \]

Substituting the known values:
\[ P_{total} = \frac{200^2}{200} = \frac{40000}{200} = 200 \, W \]

### Step 5: Conclusion
The total heat output when both heaters A and B are connected in series to a 200 V d.c. supply is 200 W.

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