First slide

combination of resistance

Question

Four identical bulbs are connected to a battery as shown in the figure. After the switch S is closed,

Moderate

A

Brightness of all bulbs will increase
B

Brightness of all bulbs will decrease
C

Brightness of all bulbs will remain unchanged
D

Brightness of B₁ and B₄ will increase and brightness of B₂ and B₃ will decrease.

Solution

initially current through each bulb, $i_{1} = \frac{V}{2 R}$
After S is closed, equivalent resistance of the circuit, $R_{C} = \frac{R \times R}{R + R} + \frac{R \times R}{R + R} = R$
So, current through each bulb, $i_{2} = \frac{1}{2} (\frac{V}{R}) = \frac{V}{2 R} = i_{1}$
Since brightness $\propto i^{2} and i_{2} = i_{1} .$ brightness of the bulbs remains unchanged.

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