Question

Bulb A rated 160 W, 40 V and Bulb B rated 40 W, 40 V are connected as shown in the diagram.
(a) Calculate the ratio V\(_1\) : V\(_2\)
(b) If the bulb A fuses, the current in the circuit remains the same. State True or False.

Hint:

In a series circuit, voltage divides in the ratio of the resistances (\(V \propto R\)), while current is constant. In a parallel circuit, current divides in the inverse ratio of the resistances (\(I \propto 1/R\)), while voltage is constant.

Answer 1

Step 1: Understanding the Concept:
In a parallel combination, the potential difference (voltage) across each component is the same.
Step 2: Detailed Explanation:
The diagram shows Bulb A and Bulb B connected in parallel across a 40 V source.
Voltmeters \(V_{1}\) and \(V_{2}\) are connected across Bulb A and Bulb B respectively.
Since they are in parallel:
Voltage across A = Voltage across B = Supply voltage = 40 V.
Therefore, \(V_{1} = 40 \text{ V}\) and \(V_{2} = 40 \text{ V}\).
Ratio = \(40 : 40 = 1 : 1\).
Step 3: Final Answer:
The ratio \(V_{1} : V_{2}\) is 1 : 1.
(b)
Step 1: Understanding the Concept:
Total current in a parallel circuit is the sum of currents in individual branches.
Step 2: Detailed Explanation:
Total Current \(I_{\text{total}} = I_{A} + I_{B}\).
If Bulb A fuses, the branch with Bulb A becomes an open circuit, and current \(I_{A}\) becomes zero.
The total current drawn from the source will now only be \(I_{B}\).
Therefore, the total main current decreases. It does not remain the same.
Step 3: Final Answer:
False. The total current in the main circuit decreases when one parallel branch fails.