Ohm’s Law (V and I Relationship)

Aim

To study the dependence of potential difference (V) across a resistor on the current (I) passing through it, and to determine its resistance. Also to plot a graph between V and I.

Apparatus and Material Required

A resistor of unknown resistance (or a piece of nichrome wire), a battery/battery eliminator (0–6 V), an ammeter (0–3 A), a voltmeter (0–5 V), a rheostat, a plug key, connecting wires, and a piece of sandpaper.

Circuit Diagram

Principle

Ohm’s law states that, at constant temperature, the current (I) flowing through a conductor is directly proportional to the potential difference (V) across its ends.
V ∝ I, so V = IR
where R is a constant for the given conductor at constant temperature, called its resistance.
R = V / I
R is measured in ohms (Ω) when V is in volts and I is in amperes. A graph of V (y-axis) against I (x-axis) for a conductor obeying Ohm’s law is a straight line through the origin, and its slope gives R.

Procedure

1. Clean the ends of all connecting wires with sandpaper to remove any insulating/oxide coating, for good contact.
2. Set up the circuit as shown: connect R, the ammeter, the rheostat, and the key in series with the battery. Connect the voltmeter in parallel across R, with its + terminal towards the battery’s + terminal.
3. Check that the ammeter is in series (same current flows through it) and the voltmeter is in parallel across R only.
4. Before inserting the key, set the rheostat to its maximum resistance position, so only a small current flows initially.
5. Insert the key and note the first pair of ammeter and voltmeter readings.
6. Using the rheostat, change the current in small, regular steps. For each setting, note the ammeter reading (I) and the corresponding voltmeter reading (V).
7. Take at least five to six sets of readings, spread across the working range of the meters.
8. Remove the key after taking all readings.
9. Record all observations in the table below.
10. Calculate R = V/I for each reading and find the mean value.
11. Plot a graph with I on the x-axis and V on the y-axis. A straight line through the origin verifies Ohm’s law; find R from its slope too.

Observations

S.N.	Ammeter Reading, I(mA)	Voltmeter Reading, V(V)	Resistance, R =V/I(Ω)
1.	100	0.5	5
2.	230	1.1	4.8
3.	300	1.6	5.3
4.	400	2.1	5.2
5.	500	2.6	5.2
6.	600	3.0	5

Calculations

Mean R = (R₁ + R₂ + R₃ + R₄ + R₅ + R₆) / 6
Using the readings above: (5+4.8+5.3+5.2+5.2+5)/6 = 5.1 Ω
Graph
V (volts) on the y-axis vs I (amperes) on the x-axis gives a straight line passing through the origin. Slope of this line = ΔV/ΔI = R.

Graph

V (volts) on the y-axis vs I (amperes) on the x-axis gives a straight line passing through the origin. Slope of this line = ΔV/ΔI = R

Results

1. The V–I graph is a straight line passing through the origin, showing that potential difference across the resistor is directly proportional to the current through it — Ohm’s law is verified.
2. Resistance of the given resistor, R = 5.1 Ω (mean value from observations / from the slope of the graph).

Precautions

1. All connections should be neat, clean, and tight.
2. The ammeter must always be connected in series, and the voltmeter in parallel.
3. Current should enter each meter from its + terminal.
4. Avoid parallax error while taking readings on the meter scales.
5. Insert the key only while taking readings; remove it immediately after, to avoid unnecessary heating of the resistor.
6. Move the rheostat in one direction only, in small steps, to get evenly spaced readings.
7. Note and correct for any zero error in the ammeter or voltmeter.

Sources of Error

1. Connecting wires and the plug key have some resistance, which isn’t accounted for.
2. Heating of the resistor during the experiment can slightly change its resistance.
3. The meters used may not be perfectly calibrated.

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Reference: NCERT Lab Manual