Question:

Consider the circuit shown below:

The circuit consists of a battery of emf ε = 12 V and internal resistance r = 2 Ω, a resistor R1 = 4 Ω, a resistor R2 = 6 Ω, and an ammeter A connected in series. The voltmeter V is connected across R2.

1. Calculate the total resistance of the circuit.

2. Determine the current flowing through the circuit.

3. Calculate the potential difference across resistor R1.

4. Determine the potential difference across resistor R2.

Answer:

1. To calculate the total resistance of the circuit, we need to consider both the resistors in series and the internal resistance of the battery.

   The total resistance (R_total) can be found using the formula:

   R_total = R1 + R2 + r

   where R1 = 4 Ω is the resistance of resistor 1, R2 = 6 Ω is the resistance of resistor 2, and r = 2 Ω is the internal resistance of the battery.

   Therefore, the total resistance (R_total) is:

   R_total = 4 Ω + 6 Ω + 2 Ω = 12 Ω

2. To determine the current flowing through the circuit, we can use Ohm's Law:

   I = ε / R_total

   where I is the current flowing through the circuit and ε is the electromotive force of the battery.

   Substituting the given values, we have:

   I = 12 V / 12 Ω = 1 A

   Therefore, the current flowing through the circuit is 1 Ampere (A).

3. To calculate the potential difference across resistor R1, we can use Ohm's Law:

   V1 = I * R1

   where V1 is the potential difference across resistor R1.

   Substituting the known values, we have:

   V1 = 1 A * 4 Ω = 4 V

   Therefore, the potential difference across resistor R1 is 4 Volts (V).

4. The potential difference across resistor R2 can be found using the voltage divider rule. According to this rule, the potential difference across each resistor in a series circuit is proportional to its resistance.

   Using the formula:

   V2 = (R2 / R_total) * ε

   where V2 is the potential difference across resistor R2.

   Substituting the known values, we have:

   V2 = (6 Ω / 12 Ω) * 12 V = 6 V

   Therefore, the potential difference across resistor R2 is 6 Volts (V).

Explanation:

This question tests your understanding of circuits, Ohm's Law, and the voltage divider rule. To determine the total resistance of the circuit, you need to add the resistances of the individual components. The current flowing through the circuit can be found using Ohm's Law, which relates current, voltage, and resistance. To calculate the potential difference across a resistor, you can use Ohm's Law by multiplying the current and resistor's resistance. The potential difference across resistor R2 is determined using the voltage divider rule, which states that the potential difference across a resistor is proportional to its resistance.