As shown in the figure below A and B are two lamps. Lamp A is rated at 12 V, 24W. Lamp B is rated at 6.0 V. When lamp B operates at its rated voltage, the current in it is 3.0 A. The values of R₁ and R₂ are chosen so that both lamps operate at their rated voltages.

Based on the information given, answer the following.

(a) Calculate the current in Lamp A.

(b) State and give reason for the reading of the Voltmeter.

(c) Calculate the resistance of R₂.

(d) Find the value of the resistance R₁.

Given,

• Voltage rating of the lamp A ($\text V_ \text A$) = 12 V
• Power rating of the lamp A ($\text P_ \text A$) = 24 W
• Voltage rating of the lamp B ($\text V_ \text B$) = 6 V
• Current passing through the lamp B ($\text I_ \text B$) = 3 A
• Battery voltage ($\text V$) = 15 V

(a) Current through the lamp A is given by,

$\text I_ \text A = \dfrac{\text P_ \text A}{\text V_ \text A} \\[1em] = \dfrac{24}{12} \\[1em] \Rightarrow \text I_ \text A = 2\ \text A$

Hence, the current in Lamp A is 2 A.

(b) Both branches (lamp A alone and lamp B in series with R₂) are in parallel, so they must have the same potential difference. For lamp A to run at its rated condition, the branch voltage must be 12 V. Hence the voltmeter connected across the branches reads 12 V.

(c) As, potential drop across lamp B branch is 12 V and is given by,

$\text V_ \text B + \text I_ \text B\text R_ \text 2 = 12 \\[1em] \text 6 + 3 \times \text R_ \text 2 = 12 \\[1em] \Rightarrow 3 \times \text R$2 = 12 - 6 \\[1em] \Rightarrow 3 \times \text R2 = 6 \\[1em] \Rightarrow \text R2 = \dfrac{6}{3} \\[1em] \Rightarrow \text R2 = 2\ \text Ω

Hence, the resistance of R₂ is 2 Ω.

(d) Current through R₁ is given by

$\text I = \text I_ \text A + \text I_ \text B \\[1em] = 2 + 3 \\[1em] = 5\ \text A \\[1em]$

And,

Potential drop across R₁ ($\text V'$) = $\text V - \text V_ \text A$ = 15 - 12 = 3 V

Also,

$\text V' = \text I \times \text R$1 \\[1em] \Rightarrow \text R1 = \dfrac{\text V'}{\text I} \\[1em] \Rightarrow \text R1 = \dfrac{3}{5} \\[1em] \Rightarrow \text R1 = 0.6\ \text Ω

Hence, the resistance of R₁ is 0.6 Ω.