Question

Verify the laws of combination (series or parallel) of resistance using meter bridge.

Hint:

For best results, choose the known resistance S from the resistance box such that the balancing point is near the center of the wire (between 40 cm and 60 cm). This minimizes the percentage error in the measurement. Always clean the ends of connecting wires with sandpaper to ensure proper electrical contact.

Answer 1

Step 1: Understanding the Concept:
The experiment involves first measuring the individual resistances of two wires, say \(R_1\) and \(R_2\), using a meter bridge. Then, these wires are connected first in series and then in parallel, and their equivalent resistances (\(R_s\) and \(R_p\)) are measured. The experimental results are then compared with the theoretical values calculated using the laws of combination of resistances.
Step 2: Key Formula and Apparatus:
Apparatus Required:
A meter bridge, a galvanometer, a resistance box, two unknown resistance wires, a primary cell (Leclanche cell or battery eliminator), a jockey, a key, and connecting wires.
Key Formula:
1. Meter Bridge Principle: It is based on the balanced Wheatstone bridge principle. If S is the resistance from the resistance box in the right gap and R is the unknown resistance in the left gap, and the balancing length from the left end is l, then: \[ R = S \left( \frac{l}{100 - l} \right) \] 2. Law of Series Combination: The theoretical equivalent resistance is the sum of individual resistances. \[ R_s (\text{theoretical}) = R_1 + R_2 \] 3. Law of Parallel Combination: The reciprocal of the theoretical equivalent resistance is the sum of the reciprocals of individual resistances. \[ \frac{1}{R_p (\text{theoretical})} = \frac{1}{R_1} + \frac{1}{R_2} \implies R_p (\text{theoretical}) = \frac{R_1 R_2}{R_1 + R_2} \] Step 3: Detailed Procedure:
Part A: Measuring Individual Resistances \(R_1\) and \(R_2\)
- Set up the circuit as per the diagram for a meter bridge.
- Connect the first resistance wire (\(R_1\)) in the left gap and the resistance box (S) in the right gap.
- Take out a suitable resistance from the resistance box S. Find the balancing length \(l_1\) by sliding the jockey.
- Calculate \(R_1 = S \left( \frac{l_1}{100 - l_1} \right)\). Take multiple readings and find the mean \(R_1\).
- Repeat the process for the second resistance wire to find the mean value of \(R_2\).
Part B: Verifying Series Combination
- Connect the two wires \(R_1\) and \(R_2\) in series and place this combination in the left gap of the meter bridge.
- Measure the equivalent resistance \(R_s (\text{experimental})\) using the same procedure as in Part A.
- Calculate the theoretical value \(R_s (\text{theoretical}) = R_1 + R_2\).
- Compare the experimental and theoretical values. A small percentage difference is expected due to experimental errors.
Part C: Verifying Parallel Combination
- Now, connect the two wires \(R_1\) and \(R_2\) in parallel and place this combination in the left gap.
- Measure the equivalent resistance \(R_p (\text{experimental})\).
- Calculate the theoretical value \(R_p (\text{theoretical}) = \frac{R_1 R_2}{R_1 + R_2}\).
- Compare the experimental and theoretical values.
Step 4: Result:
The experimental values of series resistance (\(R_s\)) and parallel resistance (\(R_p\)) are found to be in close agreement with their theoretical values. This verifies the laws of combination of resistances.