Question

A $100\text{W}$ bulb is designed to operate on a potential difference of $230\text{V}$. Find the power consumed by the bulb, if it is connected to $200\text{V}$ supply.

• A. $\frac{20000}{529}\text{W}$
• B. $\frac{40000}{529}\text{W}$
• C. $\frac{30000}{529}\text{W}$
• D. $\frac{10000}{529}\text{W}$

Answer 1

The correct option is B $\frac{40000}{529}\text{W}$

Given:
Power rating of the bulb, $P_o=100\text{W}$
Voltage rating of the bulb, $V_o=230\text{V}$

Resistance of the bulb will be

$R=\frac{V_0^2}{P_o}=\frac{(230{)}^2}{100}=529\Omega$

Now, bulb is connected with $200\text{V}$.

So, power will be

$P=\frac{V^2}{R}={\frac{200}{529}}^2$

$\therefore P=\frac{40000}{529}\text{W}$

Therefore, option $\left(\text{B}\right)$ is right.
$$\begin{array}{c}\text{Why this question?}\\ \text{Tip: If an appliance is made to run at}\\ \text{a voltage lower than the specified}\\ \text{voltage then true power consumption}\\ \text{will be less than the specified value.}\end{array}$$