Question

A heater $A$ gives out $300\text{W}$ of heat when connected to a $200\text{V}$ supply. A second heater $B$ gives out $600\text{W}$ when connected to a $200\text{V}$ supply. If a series combination of the two heaters is connected to a $200\text{V}$ supply, the heat output will be

• A. $100\text{W}$
• B. $450\text{W}$
• C. $300\text{W}$
• D. $200\text{W}$

Answer 1

The correct option is D $200\text{W}$

Power is defined as, $P=\frac{V^2}{R}$

$R=\frac{V^2}{P}$


$\therefore R_A=\frac{{\left(200\right)}^2}{300}=\frac{400}{3}\Omega$

And, $R_B=\frac{{\left(200\right)}^2}{600}=\frac{200}{3}\Omega$

Since, both are in series combination,

$\therefore R_{eq}=R_A+R_B=200\Omega$

So, power of combination will be

$P=\frac{V^2}{R_{eq}}=\frac{{\left(200\right)}^2}{200}=200\text{W}$

So, option $\left(d\right)$ is the right choice.