Wire Potential Drop Experiment Worksheet

Variation in Potential Drop with Length of Wire for a Steady Current

Objective

To study the variation in potential drop across a wire with its length when a steady current flows through it, and to verify Ohm's law.

Theory

When a steady current flows through a uniform wire of constant cross-sectional area, the potential difference across any portion of the wire is directly proportional to the length of that portion, provided physical conditions like temperature remain constant.

According to Ohm's law, the potential difference (V) across a conductor is directly proportional to the current (I) flowing through it.

Mathematically, Ohm's law is expressed as:

$V = IR$

where \(V\) is the potential difference, \(I\) is the current, and \(R\) is the resistance.

For a uniform wire, resistance is directly proportional to its length:

$R = \rho \frac{l}{A}$

where \(\rho\) is the resistivity of the material, \(l\) is the length, and \(A\) is the cross-sectional area.

Combining these equations, for a constant current and uniform wire:

$V \propto l$

This means the potential difference across any portion of the wire varies linearly with the length of that portion.

Apparatus Required

  • A uniform resistance wire (typically nichrome or constantan)
  • A meter scale
  • A battery or DC power supply
  • A voltmeter (digital preferred for precision)
  • An ammeter
  • A rheostat (or variable resistor)
  • A jockey (movable contact)
  • A key/switch
  • Connecting wires
  • A piece of sandpaper

Experimental Setup

Experimental setup showing a meter bridge with power source, ammeter, and voltmeter connections

Circuit Diagram

The circuit consists of a battery connected to a rheostat, key, ammeter, and the experimental wire in series. A voltmeter with one terminal fixed at one end of the wire and the other terminal connected to a jockey for variable positions.

In this setup:

  • Current \(I\) is measured by the ammeter
  • Potential difference \(V\) across length \(l\) is measured by the voltmeter
  • The jockey can be moved to vary the length \(l\) from one fixed end

Procedure

  1. Clean the ends of all connecting wires with sandpaper to ensure good electrical contact.
  2. Set up the circuit as shown in the diagram, connecting the battery, rheostat, key, ammeter, and experimental wire in series.
  3. Connect one terminal of the voltmeter to the fixed end of the wire (0 cm mark).
  4. Connect the other terminal of the voltmeter to the jockey, which can be moved along the wire.
  5. Close the key and adjust the rheostat to set a suitable current value (around 0.5A to 1A).
  6. Note the ammeter reading to ensure constant current throughout the experiment.
  7. Place the jockey at different positions along the wire, recording the length from the fixed end and the corresponding voltmeter reading.
  8. Take readings at regular intervals (e.g., every 10 cm) along the entire length of the wire.
  9. Repeat the procedure 2-3 times for consistency.
  10. Open the key when not taking readings to avoid unnecessary heating of the wire.

Observations

Record your observations in the following table:

S.No. Length of Wire (l) in cm Potential Difference (V) in volts Mean V (volts) V/l (V/cm)
Observation 1 Observation 2 Observation 3
1 10
2 20
3 30
4 40
5 50
6 60
7 70
8 80
9 90
10 100

Note down the constant current through the circuit: I = ________ A

Graph

Plot a graph between the length of the wire (l) on the x-axis and the potential difference (V) on the y-axis.

Graph showing linear relationship between potential difference and wire length

Calculations

Based on your observations, perform the following calculations:

1. Calculate the mean potential difference for each length

$V_{mean} = \frac{V_1 + V_2 + V_3}{3}$

2. Calculate the potential gradient (V/l) for each observation

$\text{Potential gradient} = \frac{V_{mean}}{l}$

3. Find the average potential gradient

$\text{Average potential gradient} = \frac{1}{n}\sum_{i=1}^{n}\frac{V_i}{l_i}$

4. Calculate the resistance per unit length

$\frac{R}{l} = \frac{V}{I \cdot l}$

Results

  1. The potential difference (V) across a portion of wire is directly proportional to its length (l), verifying that V ∝ l for a constant current.
  2. The potential gradient (V/l) = ________ V/cm.
  3. For the given constant current I = ________ A, the resistance per unit length of the wire is ________ Ω/cm.

Discussion

Based on your observations and calculations, discuss:

  1. The linearity of the relationship between potential difference and length of wire.
  2. Possible sources of experimental error and their effect on your results.
  3. How well your results verify Ohm's law.
  4. The significance of the constant value of V/l for a given current.

Conclusion

From this experiment, we can conclude that:

  1. The potential difference across a conductor is directly proportional to its length for a constant current, which verifies Ohm's law.
  2. The V-l graph is a straight line passing through the origin, further confirming the direct proportionality relationship.
  3. The slope of the V-l graph represents the potential gradient (V/l), which is constant for a given current.

Precautions

  1. All connections should be tight and clean to minimize contact resistance.
  2. The current should be kept constant throughout the experiment.
  3. The wire should be stretched straight and tight on the meter scale.
  4. The jockey should make gentle contact with the wire to avoid damaging it.
  5. The circuit should be closed only while taking readings to prevent heating of the wire.
  6. The ammeter and voltmeter should be connected with the correct polarity.
  7. Zero errors of all measuring instruments should be checked before starting the experiment.
  8. The experiment should be performed at a constant room temperature.
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