Physics Q36 – JEE-MAIN 2025

Home Physics Current ElectricityQuestion #58

There are '

n

' number of identical electric bulbs, each is designed to draw a power

p

independently from the mains supply. They are now joined in series across the mains supply. The total power drawn by the combination is :

Clue 1 of 3: Understand the initial condition

The power $p$ is drawn by a single bulb when connected independently to the mains supply.

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Ninja Strategy•Effect of Series Connection

Recognize that connecting identical components in series increases total resistance, leading to a decrease in total power drawn from a constant voltage source.

🧠 Full Solution Path

Step 1: Determine the resistance of a single bulb✦ Active

Let the mains supply voltage be $V$ . When a single bulb draws power $p$ independently from the mains, its resistance $R$ is given by the formula:

p = \frac{V^{2}}{R} ⟹ R = \frac{V^{2}}{p}

Step 2: Calculate the total resistance in series○ Expand

When $n$ identical bulbs, each with resistance $R$ , are connected in series across the same mains supply $V$ , the total equivalent resistance $R_{t o t a l}$ is:

R_{t o t a l} = n R

Substitute the value of $R$ from Step 1:

R_{t o t a l} = n (\frac{V^{2}}{p})

Step 3: Calculate the total power drawn by the combination○ Expand

The total power $P_{t o t a l}$ drawn by the series combination from the mains supply $V$ is:

P_{t o t a l} = \frac{V^{2}}{R_{t o t a l}}

Substitute the value of $R_{t o t a l}$ from Step 2:

P_{t o t a l} = \frac{V^{2}}{n (\frac{V^{2}}{p})} = \frac{V^{2} \cdot p}{n \cdot V^{2}} = \frac{p}{n}

💡 Teacher's Secret Hint

Remember that the voltage across the entire series combination is still the mains supply voltage $V$ .

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Physics Question 36 – JEE-MAIN 2025

Clue 1 of 3: Understand the initial condition

🧠 Full Solution Path