Question

In an electrical circuit, three resistances of 2 \(\Omega\), 4 \(\Omega\) and 6 \(\Omega\) are connected in series. A current of 2 A is flowing in the circuit. The potential difference at the ends of these resistances will be in the order:

• A. 4 V, 8 V, 12 V
• B. 6 V, 8 V, 12 V
• C. 4 V, 8 V, 10 V
• D. 2 V, 6 V, 8 V

Hint:

The potential difference across resistors in series is determined by Ohm's law \(V = I \times R\), and the current remains the same through all resistors.

Answer 1

The Correct Option is A

When resistors are connected in series, the current flowing through them is the same, and the potential difference across each resistor is determined by Ohm's law: \[ V = I \times R \] Where \(V\) is the potential difference, \(I\) is the current, and \(R\) is the resistance.
Step 1: Calculate the potential difference across each resistor.
- For the first resistor of \(2 \, \Omega\), the potential difference is: \[ V_1 = 2 \, \text{A} \times 2 \, \Omega = 4 \, \text{V} \] - For the second resistor of \(4 \, \Omega\), the potential difference is: \[ V_2 = 2 \, \text{A} \times 4 \, \Omega = 8 \, \text{V} \] - For the third resistor of \(6 \, \Omega\), the potential difference is: \[ V_3 = 2 \, \text{A} \times 6 \, \Omega = 12 \, \text{V} \]
Step 2: Analyze the options.
The potential differences at the ends of the resistances will be \( 4 \, \text{V}, 8 \, \text{V}, 12 \, \text{V} \), corresponding to option (A).

Step 3: Conclusion.
The correct order of potential differences at the ends of these resistances is \( 4 \, \text{V}, 8 \, \text{V}, 12 \, \text{V} \). The correct answer is (A).