Q) Vinita and Ahmed demonstrated a circuit that operates the two headlights and the two sidelights of a car, in their school exhibition. Based on their demonstrated circuit, answer the following questions.
(i)   State what happens when switch A is connected to
a) Position 2
b) Position 3
(ii)  Find the potential difference across each lamp when lit.
(iii) Calculate the current
a) in each 12 Ω lamp when lit.
b) In each 4 2 lamp when lit.
OR
(iv)  Show, with calculations, which type of lamp, 4.0 Ω or 12 Ω, has the higher power.

Ans:

### STEP BY STEP SOLUTION

1. a) When Switch A is connected to position 2, current will flow into both 12 Ω lamps and only these 2 lamps will glow. Current will not flow in the circuit of 4 Ω lamps and these 2 lamps will not glow.

b) When Switch A is connected to position 3, current will flow into both 4 Ω lamps and only these 2 lamps will glow. Current will not flow in the circuit of 12 Ω lamps and these 2 lamps will not glow.

2. Potential difference across each lamp:

Since in parallel circuit, the potential difference or voltage remains same across the loads.

At position 2, current flows through 12 Ω lamps and since these lamps are in parallel, therefore, the potential difference across both of these lamps will be same as supply voltage i.e. 12 V.

At position 3, current flows through 4 Ω lamps and since these lamps are in parallel, therefore, the potential difference across both of these lamps will be same as supply voltage i.e. 12 V.

Therefore, potential difference or voltage will be 12 V across each of the lamps.

3. Calculating the current:

a) In 12 Ω lamp: we know that the current is given by:

Here, the voltage across this lamp is 12 V, Resistance is 12 Ω,

Therefore current in 12 Ω lamp is: = 1 A

Therefore the current in 12 Ω will be 1 A.

b) In 4 Ω lamp: we know that the current is given by:

Here, the voltage across this lamp is 12 V, Resistance is 4 Ω,

Therefore current in 4 Ω lamp is: = 3 A

Therefore the current in 4 Ω will be 3 A.

4. Calculating the lamp with higher power:

Let’s take both lamps one by one and start with 12 Ω lamp:

we know that the power is given by:

Here, the voltage across this lamp is 12 V, Resistance is 12 Ω,

Therefore current in 12 Ω lamp is: = 12 Watt

Next, let’s take 4  Ω lamp:

we know that the power is given by:

Here, the voltage across this lamp is 12 V, Resistance is 4 Ω,

Therefore current in 4 Ω lamp is: = 36 Watt

Therefore, the 4 Ω lamp will have the higher power.

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