Question

Two lamps rated $100W$, $220V$ and $10W$, $220V$ are connected in parallel to $220V$ supply. Calculate the total current through the circuit.

Answer 1

Step 1: Given parameters

Two lamps at $220V$ having the power

$$\begin{gathered} P_1=100W \\ {P}_2=10W \end{gathered}$$

Lets $I$ is the total current through the circuit when two lamps are conned in parallel to a potential difference $V=220V$.

Step 2: Formula used

Power in a circuit is given by,

$P=V\times I$

Where, $V$ is the voltage, and $I$ is the current flowing through the conductor.

So,

$I=\frac{P}{V}$

Let $I_1$ and $I_2$ are the current flowing in each bulb.

Now the current flowing through each bulb is given by,

$\begin{array}{rcl}{I}_1& =& \frac{P_1}{V}\\ & =& \frac{100}{220}\end{array}$

and

$\begin{array}{rcl}{I}_2& =& \frac{P_2}{V}\\ & =& \frac{10}{220}\end{array}$

Now the total current($I$) is the sum of individual currents, as they are connected in parallel.

$\begin{array}{rcl}& \Rightarrow & I=I_1+I_2\\ & =& \frac{100}{220}+\frac{10}{220}\\ & =& \frac{110}{220}\\ & =& 0.5A\end{array}$

Hence, the total current flowing through the circuit is $0.5A$.