Question

An electric lamp is marked$220V,100W$. It is used for $5$hours. Calculate the total energy consumed by the lamp in $KWh$.

Answer 1

Step 1: Given data

Potential difference, $V_p=220V$

Power, $P=100W$

Time, $T=5hr$

Total energy consumed by the lamp, $E=?$

Resistance of the lamp, $R=?$

Current flowing through the lamp, $I=?$

Step 2: Formula used

$P=\frac{{V_p}^2}{R}$ ……………………(a)

$I=\frac{V_p}{R}$ ……………………….(b)

$E=I^2\times R\times T$ ………………(c)

Step 3: Calculation of the current flowing through the lamp

Substituting the given values in equation (a), we get

$$\begin{gathered} 100W=\frac{{(220V)}^2}{R} \\ R=\frac{220\times 220}{100}\Omega \\ R=484\Omega \end{gathered}$$

Substituting the value of resistance obtained above and the given value of the potential difference in equation (b), we get

$I=\frac{220V}{484\Omega }$

$I=0.4545A$ ……………………...(d)

Step 4: Calculation of the total energy consumed by the lamp

Using equation (d) and the given values in equation (c), we get

$$\begin{gathered} E={(0.4545A)}^2\times 484\Omega \times 5hr \\ E=500Wh \\ E=\frac{500}{1000}KWh \\ E=0.5KWh \end{gathered}$$

Hence, the total energy consumed by the lamp is equal to $0.5KWh$