Question

Two lamps, one rated $100W$ at $220V$, and the other $60W$ at $220V$, are connected in parallel to the electric mains supply. What current is drawn from the line if the supply voltage is $220V$?

Answer 1

Step 1: Given parameters

Two lamps at a voltage of $220V$ having power,

$$\begin{gathered} P_1=100W \\ {P}_2=60W \end{gathered}$$

Now they are connected parallel across a potential difference $V=$ $220V$.

Step 2: Formula used

According to the Joule's law of heating, the power($P$) in a circuit in terms of voltage($V$) and resistance($R$) is given by,

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

So,

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

Now the resistance for each lamp will be

$\begin{array}{rcl}{R}_1& =& \frac{V^2}{P_1}\\ & =& \frac{{\left(220\right)}^2}{100}\\ & =& 484\Omega \end{array}$

and

$\begin{array}{rcl}{R}_2& =& \frac{V^2}{P_2}\\ & =& \frac{{\left(220\right)}^2}{60}\\ & =& 806.6\Omega \end{array}$

Step 3: Calculate the equivalent resistance in parallel

Now they are connected in parallel, so the equivalent resistance is given by,

$\begin{array}{rcl}\frac{1}{R_{eq}}& =& \frac{1}{R_1}+\frac{1}{R_2}\\ & =& \frac{1}{484}+\frac{1}{806.6}\\ & =& \frac{806.6+484}{484\times 806.6}\end{array}$

So,

$R_{eq}=302.5\Omega$

Now the current($I$) in the circuit is given by

$\begin{array}{rcl}I& =& \frac{V}{R_{eq}}\\ & =& \frac{220}{302.5}\\ & =& 0.73A\end{array}$

Hence current drawn from the line is $0.73A$.