Meter Bridge Experiment

TO FIND THE RESISTANCE OF A GIVEN WIRE USING METRE BRIDGE AND HENCE DETERMINE THE SPECIFIC RESISTANCE OF ITS MATERIAL

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1. AIM

To determine the resistance of a given wire using a meter bridge and calculate the specific resistance (resistivity) of its material.

2. APPARATUS USED

  • Meter bridge with jockey
  • Galvanometer
  • Resistance box (standard resistance)
  • Unknown resistance wire
  • Leclanche cell or battery
  • Commutator or plug key
  • Screw gauge
  • Meter scale
  • Connecting wires
  • Sandpaper
  • One-way key

3. DIAGRAM

Meter Bridge Circuit Diagram

Meter Bridge Circuit Diagram:

P l Q o------------------------------------o | | | | X R | | | | | | Battery + Key Galvanometer

4. THEORY

The meter bridge works on the principle of the Wheatstone bridge. It consists of a one-meter long uniform wire of constantan or manganin fixed on a wooden board with a scale marked from 0 to 100 cm. The wire is connected to two thick copper strips with gap at the center.

In a balanced Wheatstone bridge:

$\frac{P}{Q} = \frac{R}{S}$

Where P, Q, R, and S are resistances in the four arms.

In the meter bridge setup, if X is the unknown resistance, R is the known resistance from the resistance box, and l is the balancing length (in cm) from the left end, then:

$\frac{X}{R} = \frac{l}{(100-l)}$

This is because the resistance of a wire is proportional to its length when the material and cross-sectional area are uniform.

The specific resistance or resistivity (ρ) of the material is given by:

$\rho = \frac{RA}{L}$

Where:

  • R is the resistance of the wire (in Ω)
  • A is the cross-sectional area of the wire (in m²)
  • L is the length of the wire (in m)

5. FORMULA

1. Resistance of the unknown wire (X):

$X = R \times \frac{l}{(100-l)}$

Where:

  • X = Unknown resistance (Ω)
  • R = Standard resistance from resistance box (Ω)
  • l = Balancing length from left end (cm)

2. Specific resistance or resistivity (ρ):

$\rho = \frac{\pi r^2 X}{L}$

Where:

  • ρ = Specific resistance (Ω·m)
  • r = Radius of the wire (m)
  • X = Resistance of the wire (Ω)
  • L = Length of the wire (m)

6. PROCEDURE

  1. Set up the circuit:
    • Place the meter bridge on a level table.
    • Connect the unknown resistance (X) between terminals on the left gap.
    • Connect the resistance box (R) between terminals on the right gap.
    • Connect the battery and key in series with the meter bridge.
    • Connect the galvanometer between the jockey and the middle terminal.
  2. Clean the ends of all connecting wires with sandpaper to ensure good electrical contact.
  3. Record the length (L) of the unknown resistance wire using a meter scale.
  4. Measure the diameter of the unknown wire at different places using a screw gauge and calculate the average diameter and radius.
  5. Set a suitable resistance (R) in the resistance box (typically between 1-5 Ω).
  6. Close the key and place the jockey at the middle of the wire (near 50 cm mark).
  7. Move the jockey along the wire to find the null point (where galvanometer shows zero deflection).
  8. Record the position (l) of the jockey where the galvanometer shows zero deflection.
  9. Repeat steps 7-8 at least five times with different values of standard resistance R.
  10. Reverse the positions of the unknown resistance and standard resistance to eliminate errors due to end resistances, and repeat the experiment.
  11. Calculate the unknown resistance (X) using the formula $X = R \times \frac{l}{(100-l)}$.
  12. Calculate the resistivity (ρ) using the formula $\rho = \frac{\pi r^2 X}{L}$.

7. OBSERVATION TABLE

A. Measurement of diameter of the given wire:

S.No. Screw Gauge Reading Diameter (d) (m)
MSR (mm) CSR × LC d = MSR + CSR × LC (mm)
1.
2.
3.
4.
5.

Mean diameter (d) = ___________ m

Mean radius (r) = d/2 = ___________ m

Length of the wire (L) = ___________ m

B. Determination of resistance (X):

S.No. Position of unknown resistance (X) Resistance from box (R) (Ω) Balancing length (l) (cm) (100-l) (cm) X = R × [l/(100-l)] (Ω)
1. Left gap
2. Left gap
3. Left gap
4. Left gap
5. Left gap
6. Right gap
7. Right gap
8. Right gap
9. Right gap
10. Right gap

Mean value of X = ___________ Ω

8. CALCULATIONS

1. Cross-sectional area of the wire:

$A = \pi r^2 = \pi \times (_________)^2 = ___________ \text{ m}^2$

2. Resistance of the wire:

$\text{Mean value of } X = ___________ \Omega$

3. Specific resistance (resistivity):

$\rho = \frac{XA}{L}$
$\rho = \frac{(_______) \Omega \times (_______) \text{ m}^2}{(_______) \text{ m}}$
$\rho = ___________ \Omega \cdot \text{m}$

9. RESULT

  1. The resistance of the given wire is ___________ Ω.
  2. The specific resistance (resistivity) of the material of the wire is ___________ Ω·m.
  3. The material of the wire could be ___________ (based on the resistivity value).

10. PRECAUTIONS

  1. All connections should be tight, clean, and without loops.
  2. The jockey should be moved gently over the wire to avoid damaging it.
  3. The jockey should not be kept pressed on the wire for a long time to avoid heating effects.
  4. The bridge wire should be uniform in cross-section and free from kinks or damage.
  5. The resistance box plugs should be tight and clean.
  6. To avoid errors due to thermal emf, the key in the battery circuit should be closed only when taking observations.
  7. The ends of the bridge wire should be carefully soldered to the copper strips.
  8. Proper zero adjustment of the galvanometer should be ensured before starting the experiment.
  9. The galvanometer should be protected from overloading by starting with the jockey at the middle of the wire.
  10. The battery used should have a steady emf.

11. SOURCES OF ERROR

  1. End resistance error: The resistance of the connecting strips and contacts at the ends of the bridge wire.
  2. Non-uniformity of the bridge wire: Variations in cross-section or material properties.
  3. Thermal EMF: Generated at junctions of dissimilar metals in the circuit.
  4. Temperature variations: Affecting the resistivity of the wire during measurement.
  5. Parallax error: When reading the position of the jockey on the scale.
  6. Contact resistance: Between the jockey and the bridge wire.
  7. Resistance of connecting wires: Not accounted for in calculations.
  8. Inaccurate measurement of wire dimensions: Errors in measuring diameter or length.
  9. Zero error in measuring instruments: Screw gauge or meter scale.
  10. Sensitivity of the galvanometer: Limiting the precision of the null point detection.

12. VIVA VOCE QUESTIONS

Q: What is the principle of a meter bridge?

A: The meter bridge works on the principle of the Wheatstone bridge, where at balance, the ratio of resistances in the four arms follows P/Q = R/S.

Q: Why is the meter bridge wire made of constantan or manganin?

A: These materials have high resistivity, low temperature coefficient of resistance, and are not easily oxidized, ensuring stability and accuracy in measurements.

Q: Why do we take readings by shifting the unknown resistance from left to right gap?

A: To eliminate errors due to end resistances and any non-uniformity in the bridge wire.

Q: What is the effect of temperature on resistance?

A: For most metals, resistance increases with temperature due to increased thermal vibrations of atoms, which impede electron flow.

Q: What happens if the jockey is pressed too hard on the wire?

A: It can damage the wire, create local heating, and alter the resistance value, affecting the accuracy of measurements.

Q: Why should the battery key be closed only while taking observations?

A: To prevent heating of the circuit components and to avoid unwanted thermal EMFs.

Q: What is the relation between resistance and resistivity?

A: $R = \frac{\rho L}{A}$, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area.

Q: How does the cross-sectional area of a wire affect its resistance?

A: Resistance is inversely proportional to cross-sectional area. As area increases, resistance decreases.

Q: What are the typical units of resistivity?

A: Ohm-meter (Ω·m) or Ohm-centimeter (Ω·cm).

Q: Why is a high resistance galvanometer preferred in this experiment?

A: A high resistance galvanometer draws less current from the circuit, causing minimal disturbance to the balanced condition.

Q: What is the significance of the null point in this experiment?

A: The null point represents the balance condition where no current flows through the galvanometer, allowing us to use the balanced bridge equation to calculate the unknown resistance.

Q: How would you identify a material based on its resistivity value?

A: By comparing the experimental value with standard resistivity values of different materials. For example:

  • Copper: ~1.68 × 10-8 Ω·m
  • Aluminum: ~2.65 × 10-8 Ω·m
  • Nichrome: ~1.10 × 10-6 Ω·m
  • Constantan: ~4.9 × 10-7 Ω·m
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