A potentiometer is connected between A & B & the balance point is obtained at 203.6 cm.When the end of the potentiometer is connected to B is shifted to C,then the balance point is obtained at 24.6cm.If now the potentiometer be connected between B & C,the balance point will be at?

To solve this problem, we need to understand how a potentiometer works and how the balance points relate to the lengths of the wire segments involved. A potentiometer measures the potential difference (voltage) across two points in a circuit by balancing it against a known voltage. The balance point indicates the length of the wire that corresponds to that voltage. Let's break down the information given and find the balance point when the potentiometer is connected between points B and C.

Understanding the Setup

Initially, the potentiometer is connected between points A and B, and the balance point is found at 203.6 cm. This means that the potential difference between A and B corresponds to the voltage drop over 203.6 cm of the potentiometer wire.

Next, when the end of the potentiometer connected to B is shifted to point C, the new balance point is at 24.6 cm. This indicates that the potential difference between B and C corresponds to the voltage drop over 24.6 cm of the potentiometer wire.

Analyzing the Lengths

Let's denote the following:

• L_AB = Length of the potentiometer wire between A and B = 203.6 cm
• L_BC = Length of the potentiometer wire between B and C = 24.6 cm

When we connect the potentiometer between B and C, we want to find the new balance point, which we can denote as L_BC' (the length at which the balance occurs between B and C).

Finding the Balance Point

To find L_BC', we can use the concept of proportionality in the lengths of the wire. The potential difference across the entire length from A to B is proportional to the length of the wire used. Since we have the lengths for both segments, we can set up a ratio:

We know that:

• Voltage across A and B is proportional to 203.6 cm
• Voltage across B and C is proportional to 24.6 cm

Now, when we connect the potentiometer between B and C, we can express the relationship as:

L_BC' = (L_BC / L_AB) * L_AB

Substituting the known values:

L_BC' = (24.6 cm / 203.6 cm) * 203.6 cm

However, since we are looking for the balance point when connected between B and C, we can directly use the length of 24.6 cm as the balance point since it already represents the voltage drop across that segment.

Final Calculation

Thus, when the potentiometer is connected between B and C, the balance point will be at:

L_BC' = 24.6 cm

This means that the potential difference between B and C is balanced at the same length of 24.6 cm, confirming that the setup is consistent with the principles of a potentiometer. The balance point indicates the voltage drop across the wire segment, which is directly proportional to the length of wire used.