Question

If two heaters, each of power 1 kW are connected in parallel to a 250 V supply, their combined rate of heating will be

• A. 1 kW
• B. 2 kW
• C. 5 kW
• D. 250 kW

Answer 1

The correct option is B

2 kW

Step 1: Given data

Power of one heater = 1000W

The voltage of the power supply = 250V (in parallel connection voltage remains same)

Step 2: Calculate resistance when connected in parallel-

We know that, $P=\frac{V^2}{R}$

$$\begin{gathered} \Rightarrow 1000=\frac{250\times 250}{R} \\ \Rightarrow R=\frac{250\times 250}{1000}\Omega \\ \Rightarrow R=\frac{250}{4}\Omega \end{gathered}$$

When two resistance in parallel so equivalent resistance will be

$$\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{R} \\ \Rightarrow R_{eq}=\frac{R}{2}=\frac{250}{8}=\frac{125}{4}\Omega \end{gathered}$$

Step 3: Calculate the combined rate of heating-

The rate of heating will be the combined power dissipated

$$\begin{gathered} \therefore Rateofheating=\frac{V^2}{R_{eq}} \\ \Rightarrow Rateofheating=\frac{250\times 250\times 4}{125}=2000=2kW \end{gathered}$$

Thus, the combined rate of heating will be 2 kW.

Hence, option B is correct.