Question

Out of two bulbs $50Wand100W$, which one will grow brighter if (SAT) connected in series and when connected in parallel?

Answer 1

Step 1: Given data

two bulbs of $50Wand100W$

Step 2: Formula used

$$\begin{gathered} R=\frac{V^2}{P}[whereR=resis\tan ce,V=volatge,P=power] \\ I=\frac{V}{R_s}[whereI=currentflowinginthecircuitinseries,R_s=resis\tan ceinseries] \end{gathered}$$

Step 3: Calculating current

As we know from Ohm’s law current I is inversely related to the resistance R of a circuit. So, here for the given rated voltage bulb, the resistance of the 50 W bulb will be more than that of the 100W bulb.
As resistance is given by: $R=\frac{V^2}{P}$

The total current flowing in the circuit in series is given by: $I=\frac{V}{R_s}$

1. Since the same current is passing through each bulb when connected in series, $50W$ bulb will glow brighter as power is given by the product of the square of current and resistance, which is more in the case of $50W$ bulb.
2. Also, when these bulbs are connected in parallel, $100W$ bulb will glow much brighter as power here is given as a product of the square of voltage and resistance, which is more in the case of $100W$bulb.

Hence, the $50W$ bulb will glow brighter when connected in series and the $100W$ bulb will glow brighter when connected in parallel.