Question

Fifty lamps each of resistance $100ohm$ are connected in parallel across a $220V$main.

Find (a) the power consumed in watts, and (b) the cost of operating the lamps for $20$ hours at $10$ paise per $KWh$.

Answer 1

Step 1:Given

A $220volts$main is used to connect $50$ bulbs in parallel, each with a resistance of $100ohm.$

Step 2:Finding equivalent resistance

The equivalent resistance is:-

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+......+\frac{1}{R_{50}}$

$$\begin{gathered} \frac{1}{R}=\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100} \\ \frac{1}{R}=\frac{50}{100} \\ R=2ohm \end{gathered}$$

Step 3: Calculating power consumed

$$\begin{gathered} P=V^2/R \\ P={\left(220\right)}^2/2 \\ P=24200W \end{gathered}$$

Step 4:Cost of operating the lamps for $20$ hours at $10$ paise per kWh

$$\begin{gathered} P=24.2kW \\ Time=20 \\ Cost\left(rs\right)=\frac{10}{100}=0.1rs \end{gathered}$$

Cost= Power $\times$time $\times$cost (in rs)

$=24.2\times 20\times 0.1$

$=48.40Rs$

Hence, the power consumed is $24.2kW$ and the cost is $48.40Rs$.