https://file.aiquickdraw.com/mathbot/file/1727425952823bczwqpbg.jpg

Let's analyze the circuit step by step.

### Given Information:
- A current of \( 2A \) flows through the resistor of \( 5\Omega \) in the parallel branch.
- There are three resistors: \( R \), \( 2R \), and \( 5\Omega \).

### Objective:
Find the potential difference between points X and Y.

### Steps:

1. **Calculate the voltage across the 5Ω resistor:**
   The voltage across any resistor \( V \) can be found using Ohm's Law:
   \[
   V = IR
   \]
   Here, \( I = 2A \) and \( R = 5\Omega \), so:
   \[
   V = 2A \times 5\Omega = 10V
   \]

   Therefore, the potential difference across the parallel branch is \( 10V \).

2. **Interpretation for the overall circuit:**
   Since the resistors \( 5\Omega \) and \( 2R \) are in parallel, the voltage across the entire parallel section must also be \( 10V \) (as both branches of a parallel circuit share the same voltage).

Thus, the potential difference between points X and Y is exactly \( 10V \).

### Correct Answer:
\[
\boxed{a) \ 10V}
\]

Would you like further details or have any questions? Here are some related questions to deepen your understanding:

1. How would the potential difference change if the resistance in one branch increased?
2. What would happen to the current if the resistances were rearranged in series?
3. Can you calculate the total equivalent resistance of the circuit?
4. How does the parallel arrangement affect current distribution?
5. What would the voltage be if the current in the parallel branch was different?

**Tip:** In parallel circuits, the voltage remains the same across all branches, but the current divides based on the resistance.

In the opposite circuit, the potential difference between the two points X, Y is?

This problem helps you calculate the potential difference between two points in a parallel circuit with a 5Ω resistor and a 2A current. Using Ohm's Law, find the voltage across the branches, which is essential for understanding circuit behavior. Suitable for Grades 10-12.

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