Question

As shown in the figure above, A and B are two lamps. Lamp A is rated at 12 V, 24 W. 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.

1. Calculate the current in Lamp A.
2. State and give reason for the reading of the voltmeter.
3. Calculate the resistance of R₂.
4. Find the value of the resistance R₁.

Answer 1

1. Use of P = IV
   I = P ÷ V = 24 W ÷ 12 V
   Current in lamp A = 2 A
2. Voltmeter reading = 12 V
   Lamp A and Lamp B are in parallel.
   Hence, the potential difference across the arm containing A = Potential difference across the arm containing B.
   = 12 V  ...(from i)
3. Potential difference across R₂ + Potential difference across B = 12 V
   Potential difference across B = 6 V  ...(given)
   Hence potential difference across R₂ = 12 V − 6 V = 6 V
   Current through R₂ = Current through B = 3 A  ...(given)
   Use of R = `V/I`
   R₂ = `(6V)/(3A)` = 2Ω
4. Current through R₁ = Total Current = 3A + 2A = 5A
   Potential difference across R₁ = 15 V − 12 V = 3V
   R₁ = `(3V)/(5A)` = 0.6 Ω