Question

The total length of potentiometer wire AB is $50$ cm in the arrangement as shown in figure. If P is the point where the galvanometer shows zero reading then the length AP is _________ cm.

• A. 30
• B. 25
• C. 15
• D. 20

Hint:

In bridge balance problems, the ratio of the components on the left must equal the ratio of the components on the right.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
When the galvanometer shows zero reading, the potential at point P is equal to the potential at the junction between the $6 \Omega$ and $4 \Omega$ resistors. This creates a balanced Wheatstone bridge condition between the resistors and the segments of the potentiometer wire.

Step 2: Key Formula or Approach:
For a balanced condition:
\[ \frac{R_1}{R_2} = \frac{L_{AP}}{L_{PB}} \]
Where \( L_{AB} = L_{AP} + L_{PB} = 50 \) cm.

Step 3: Detailed Explanation:
Let \( L_{AP} = x \) cm. Then \( L_{PB} = (50 - x) \) cm.
The resistance of a wire segment is proportional to its length.
Given resistors are \( R_1 = 6 \Omega \) and \( R_2 = 4 \Omega \).
At balance:
\[ \frac{6}{x} = \frac{4}{50 - x} \]
\[ 6(50 - x) = 4x \]
\[ 300 - 6x = 4x \]
\[ 10x = 300 \]
\[ x = 30 \text{ cm} \]

Step 4: Final Answer:
The length AP is 30 cm.