The balance point in metre bridge experiment is obtained at 30 cm from the left. If the right gap contains 3.5 W, what is the resistance in the left gap?

To find the resistance in the left gap of a metre bridge when the balance point is at 30 cm from the left and the right gap contains a resistance of 3.5 ohms, we can use the principles of the metre bridge experiment, which is based on the concept of a Wheatstone bridge. This setup allows us to determine unknown resistances by balancing the bridge.

Understanding the Metre Bridge Setup

A metre bridge consists of a wire of uniform cross-section, typically 1 meter long, with a sliding contact that helps find the balance point. When the bridge is balanced, the ratio of the resistances on either side of the bridge is equal to the ratio of the lengths from the sliding contact to the ends of the bridge.

Applying the Balance Condition

The balance condition can be expressed mathematically as:

• R1 / R2 = L1 / L2

Where:

• R1 is the resistance in the left gap (unknown).
• R2 is the resistance in the right gap (3.5 ohms).
• L1 is the length from the left end to the balance point (30 cm).
• L2 is the length from the balance point to the right end (70 cm, since the total length is 100 cm).

Calculating the Resistance

Now, substituting the known values into the balance condition:

• R1 / 3.5 = 30 / 70

We can simplify the right side of the equation:

• 30 / 70 = 3 / 7

Now, substituting this back into the equation gives:

• R1 / 3.5 = 3 / 7

To find R1, we can cross-multiply:

• R1 = 3.5 * (3 / 7)

Now, performing the multiplication:

• R1 = 3.5 * 0.4286 (approximately)
• R1 ≈ 1.5 ohms

Final Result

Thus, the resistance in the left gap is approximately 1.5 ohms. This method illustrates how the metre bridge can effectively determine unknown resistances using the principles of balance and proportionality.