Answer :
To solve the questions about Arun's series circuit, let's break it down step-by-step.
a) Calculate the voltage across one lamp.
In a series circuit, the total voltage of the battery is divided among the components. Here, you have a 6 V battery and the voltage across one buzzer is given as 1 V. The circuit has two identical buzzers and two identical lamps.
Both buzzers together have a total voltage of:
- Voltage across two buzzers = 1 V + 1 V = 2 V.
The total voltage in the circuit is 6 V, so the remaining voltage must be across the lamps:
- Voltage across two lamps = Total voltage - Voltage across buzzers = 6 V - 2 V = 4 V.
Since there are two identical lamps, the voltage across one lamp is half the total voltage across both lamps:
- Voltage across one lamp = [tex]\frac{4 \text{ V}}{2} = 2 \text{ V}.[/tex]
b) Arun adds another 6 V battery in series with the first battery.
When a battery is added in series, the total voltage increases. Let's address the two parts:
i) State the voltage across one of the buzzers when the second battery is added.
The total voltage in the circuit now becomes:
- Total voltage = 6 V (first battery) + 6 V (second battery) = 12 V.
Since the circuit components continue to work properly and are identical, the voltages will equally scale with the new total voltage:
- Previously, the total across buzzers was 2 V for a 6 V supply, so it doubles with a 12 V supply:
- Voltage across two buzzers = 4 V.
- Previously, the total across buzzers was 2 V for a 6 V supply, so it doubles with a 12 V supply:
Therefore, the voltage across one buzzer is:
- Voltage across one buzzer = [tex]\frac{4 \text{ V}}{2} = 2 \text{ V}.[/tex]
ii) State the effect on the current in the circuit of adding the second battery.
In a series circuit, adding an additional power supply increases the total voltage.
From Ohm’s Law ([tex]V = IR[/tex]), if the resistance remains constant and the voltage increases, the current in the circuit will also increase proportionally.
Therefore, adding the second battery will increase the current through the circuit components.
