Question

An electric bulb is rated at $200V-100W$. What is its resistance? Five such bulbs burn for $4hours$. Calculate the cost of electrical energy consumed if the rate is $₹5perunit$.

Answer 1

Step 1 - Given data

1. Voltage $V=200V$
2. Power $P=100W$
3. Time $t=4h$
4. Number of bulbs $n=5$
5. Rate $r=₹5/unit$ or $r=₹5/kWh$

(Note: $1unit=1kWh$)

Step 2 - Finding the resistance

Consider the resistance of the bulb is $R$.

So, the resistance can be calculated as

$$\begin{gathered} R=\frac{V^2}{P} \\ R=\frac{{(200V)}^2}{(100W)} \\ R=\frac{40000}{100} \\ R=400\Omega \end{gathered}$$

Step 3 - Finding the energy consumed by one bulb

Consider the energy consumed by one bulb is $E_1$.

So, $E_1$ can be calculated as

$$\begin{gathered} E_1=P\times t \\ {E}_1=(100W)\times (4h) \\ {E}_1=(0.1kW)\times (4h) \\ {E}_1=0.4kWh \end{gathered}$$

Step 4 - Finding the energy consumed by five bulb

Consider the total consumed energy is $E$.

So, the total energy consumed by five bulbs can be calculated as

$$\begin{gathered} E=n\times E_1 \\ E=5\times 0.4kWh \\ E=2kWh \end{gathered}$$

Step 5 - Finding the cost of electric energy consumed

Consider the total cost is $R$.

So, the total cost can be calculated as below

$$\begin{gathered} R=E\times r \\ R=(2kWh)\times (₹5/kWh) \\ R=₹10 \end{gathered}$$

Thus, the resistance is $400\Omega$ and the cost of electric energy consumed is$₹10$.