Study the Variation in Potential Drop
Aim
To study the variation in potential drop with length of a wire for a steady current.
Apparatus and Material Required
- Potentiometer,
- battery eliminator of constant voltage,
- voltmeter,
- ammeter,
- plug key,
- jockey,
- rheostat,
- connecting wires, etc.
Principle
If a steady current is flowing through a wire with uniform cross section and constant resistance per unit length, potential drop \(V\) across two points of the wire is directly proportional to the length \(l\) between those two points.
Mathematically, \[V \propto l\]
Procedure
- Set up the electric circuit as per the adjoining diagram.
- Connect the positive terminal of the battery to point \(P\) (zero length) of the potentiometer through a plug key.
- Connect negative end of the battery to the other end \(Q\) (Full length) of the potentiometer wire through an ammeter, and a rheostat. Connect the negative terminal of the ammeter with negative terminal of the battery.
- Connect the positive terminal of the voltmeter to point \(P\) and other end to a jockey \(J\).
- Now close the key K and press the jockey at point \(Q\). Adjust the rheostat to get full scale deflection in voltmeter.
- Voltmeter will show zero deflection when jockey is pressed at point \(P\).
- Press the jockey at 150 cm and note down the corresponding reading in voltmeter.
- Repeat the step 7 for various lengths of the wire like 200 cm, 250 cm, 300 cm, 400 cm.
- Record the readings in a table.
Observations
Range of the voltmeter = 0 to 5 \(V\)
Range of the ammeter = 0 to 5 \(A\)
Zero error = 0 \(V\) in voltmeter and 0 \(A\) in ammeter
| S.N. | Length of wire over which potential drop is measured, \(l\) (cm) | Voltmeter Reading, \(V\) (V) | \(\phi = \frac{V}{l}\) (V/cm) |
|---|---|---|---|
| 1 | 150 | 1 | 0.009 |
| 2 | 200 | 1.5 | 0.009 |
| 3 | 250 | 2.1 | 0.008 |
| 4 | 300 | 2.5 | 0.008 |
| 5 | 400 | 3.3 | 0.008 |
| Mean | 0.008 |
Calculations
Calculate the mean value of ratio \(\phi = \frac{V}{l}\). \[\phi_{mean} = \frac{\phi_{1}+\phi_{2}+\phi_{3}+\phi_{4}+\phi_{5}}{5}\]
\[\phi_{mean} =0.008 V\cdot cm^{-1}\]
It is the potential gradient of the wire.
Plotting Graph
Results
Value of the potential gradient of the wire is almost constant.
Precautions
- There should be no zero error either in voltmeter or ammeter. If there is, correct it.
- Current across the potentiometer must remain the same. Monitor ammeter continuously and make suitable adjustments with help of the rheostat to ensure uniform current. Also, current should be drawn intermittently for short duration of time.
- Press the jockey gently, otherwise it can change the cross sectional area of the wire.
- Uniformity of the wire is a must. If it is not uniform, the potential gradient will not be same throughout it.
Sources of error
- Non-uniformity of the wire.
- Heating of the wire with time.
Discussion
- The potentiometer wire is connected firmly to thick copper strips after every 100 cm of its length of 400 or 1000 cm. However, these small sections of wire do not contribute to the total length of the potentiometer wire as copper is very good conductor.
- Potentiometer has the advantage that it draws no current from the voltage source being measured. Thus, internal resistance of the source does not affect the current.
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