High School

Arun has a series circuit with a 6 V battery, two identical buzzers, and two identical lamps.

The voltage across one buzzer is 1 V.

a) Calculate the voltage across one lamp.

b) Arun adds another 6 V battery in series with the first battery. All the components continue to work properly.

i) State the voltage across one of the buzzers when the second battery is added.

ii) State the effect on the current in the circuit of adding the second battery.

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.

  1. Both buzzers together have a total voltage of:

    • Voltage across two buzzers = 1 V + 1 V = 2 V.
  2. 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.
  3. 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.

  1. The total voltage in the circuit now becomes:

    • Total voltage = 6 V (first battery) + 6 V (second battery) = 12 V.
  2. 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.
  3. 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.

  1. In a series circuit, adding an additional power supply increases the total voltage.

  2. 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.

  3. Therefore, adding the second battery will increase the current through the circuit components.