Electricity: Experimental Verification of Ohm's Law and Rheostats Class 10

In physics, theoretical laws are meaningless until verified by hands-on laboratory measurement. In 1827, Georg Simon Ohm did not deduce $V = IR$ from pure thought; he painstakingly assembled electric cells, varied current flow with metallic wires, and measured potential differences across conductors.

In CBSE Class 10 Science, Chapter 11 (Electricity), the laboratory verification of Ohm's Law is a cornerstone of practical-based questions (Section B and Section C). Examiners regularly test the exact circuit schematic, the function of a rheostat, the difference between $V-I$ and $I-V$ graph slopes, and why real-world conductors deviate from Ohm's Law when they overheat.

In this master guide, we break down the complete experimental protocol and graphical analysis.

What You Will Learn

• Complete circuit diagram for the experimental verification of Ohm's Law
• Correct placement and polarity of the Ammeter and Voltmeter
• The precise function of a Rheostat (Variable Resistor) in the circuit
• Graphical analysis: Slope of $V-I$ graph ($R$) vs. Slope of $I-V$ graph ($1/R$)
• Why the $V-I$ graph bends into a curve if the wire overheats
• Ohmic vs. Non-Ohmic Conductors
• Practical-based board exam questions and laboratory precautions

1. The Circuit Setup for Ohm's Law Verification

To verify Ohm's Law experimentally, connect the following components in a closed circuit:

                  +--- Battery (Cells) ---+
                  |                       |
                  |     ( • ) Plug Key    |
                  |                       |
                  +---( A ) Ammeter ------+
                  |    (In Series)        |
                  |                       |
            +-----+                       +-----+
            |                                   |
            +-----------/\/\/\/\/\--------------+
            |          Nichrome Wire (R)        |
            |                                   |
            +--------------( V )----------------+
                         Voltmeter
                        (In Parallel)
            |                                   |
            +------------/\/\/\/\/\-------------+
                       Rheostat (Rh)

Components and Connection Rules:

1. Nichrome Resistor Wire ($R$): The conducting specimen across which $V$ and $I$ are measured.
2. Ammeter ($A$): Connected strictly in SERIES with the resistor wire to measure current ($I$). Its positive terminal connects toward the battery's positive terminal.
3. Voltmeter ($V$): Connected strictly in PARALLEL across the two ends of the nichrome wire to measure potential difference ($V$).
4. Rheostat ($Rh$): Connected in series to adjust and vary the current smoothly.
5. Plug Key & Battery: Supplies power and opens/closes the circuit.

2. The Crucial Role of the Rheostat (Variable Resistor)

The Question: What is the specific function of a rheostat in the Ohm's Law verification circuit?

• In a laboratory experiment, we need to take multiple pairs of readings for voltage ($V$) and current ($I$) to plot a graph.
• How can you change the current without changing the battery cells each time?
• The Function of a Rheostat:

  <u>A rheostat (variable resistor) allows you to smoothly regulate and vary the electric current flowing through the circuit WITHOUT changing the voltage of the source battery!</u>

• By sliding the rheostat contact, you change its internal resistance, altering the total circuit current and providing a fresh set of $(V, I)$ values.

3. Graphical Analysis: $V-I$ vs. $I-V$ Graphs

In board exams, pay close attention to which variable is on the vertical $y$-axis:

          Case A: V-I Graph                                Case B: I-V Graph
       Potential Difference (V)                         Current (I)
            ^              /                                 ^              /
            |             / Slope = ΔV / ΔI                  |             / Slope = ΔI / ΔV
            |            /        = R                        |            /        = 1 / R
            |           /                                    |           /
            +----------+--------> Current (I)                +----------+--------> Voltage (V)
            Slope DIRECTLY gives RESISTANCE R!               Slope gives RECIPROCAL (1 / R)!

1. When $V$ is on the $y$-axis and $I$ is on the $x$-axis: $\mathbf{\text{Slope} = \frac{\Delta V}{\Delta I} = R\text{ (Resistance)}}$ A steeper slope indicates a higher resistance.
2. When $I$ is on the $y$-axis and $V$ is on the $x$-axis: $\mathbf{\text{Slope} = \frac{\Delta I}{\Delta V} = \frac{1}{R}\text{ (Conductance)}}$ A steeper slope indicates a LOWER resistance!

4. Why Does the $V-I$ Graph Bend When a Wire Overheats?

Ohm's Law states that $V \propto I$ provided temperature remains constant:

• If current is allowed to flow continuously through a thin wire for too long, Joule heating ($H = I^2Rt$) raises the wire's temperature.
• For pure metallic conductors, resistance increases as temperature rises!
• As resistance increases, a higher voltage is needed to push the same current:
  • <u>The V-I graph ceases to be a straight line and curves upwards! The conductor becomes NON-OHMIC at high temperatures.</u>

Ohmic vs. Non-Ohmic Conductors:

• Ohmic Conductors: Obey Ohm's law ($V-I$ graph is a straight line through origin at constant temperature, e.g., copper wire, nichrome wire).
• Non-Ohmic Conductors: Do not obey Ohm's law ($V-I$ graph is non-linear/curved, e.g., incandescent bulb filament, semiconductor diodes, electrolytes).

5. Summary and Examination Tips

Exam Tip: In practical-based questions asking for laboratory precautions:

1. Always remove the plug key between successive readings to prevent the wire from heating up, which would alter its resistance!
2. Ensure connecting wires have their ends cleaned with sandpaper to remove insulating oxide layers.

Common Mistake: Calculating resistance from an $I-V$ graph by taking $\Delta y / \Delta x$ directly without inverting. If $I$ is on the vertical axis, $\text{Slope} = 1/R$, so $R = 1 / \text{Slope}$!