Question

An electric bulb is rated $220V$ and $100W$. When it is operated on $110V$, what will be the power consumed?

Answer 1

Step1: Given data

1. The power rating of the bulb is $P=100W.$
2. The voltage rating of the bulb is $V=220V.$
3. Power has to find at voltage $110V$.

Step2: Electrical power

1. Electrical power is the energy consumed by a circuit in a unit time.
2. The power of an electrical circuit is defined by the form, $P=\frac{V^2}{R}$, where, V is the voltage and R is the resistance of the circuit.

Step3: Diagram

Step4: Finding the resistance

As we know, $P=\frac{V^2}{R}$.

So, the resistance of the circuit is $R=\frac{V^2}{P}$.

Or

$$\begin{gathered} R=\frac{V^2}{P}=\frac{{220}^2}{100}=\frac{48400}{100}=484 \\ orR=484ohm. \end{gathered}$$

Step5: Finding the power at a voltage $110V$

The power of an electrical circuit is $P=\frac{V^2}{R}$.

So,

$$\begin{gathered} P=\frac{V^2}{R}=\frac{{110}^2}{484}=25 \\ orP=25watts \end{gathered}$$

Therefore, the power consumed by the circuit at a voltage of 110 volts is $25watt.$