Experiment: Verifying Ohm's Law with Voltmeter-Ammeter - Tenth Grade Science
Ohm's law is the foundational relationship governing electrical conduction in ohmic circuits. In this practical investigation, students assemble a complete DC electrical test circuit using an unknown resistive wire, a variable DC source, an ammeter, a voltmeter, and a rheostat. By systematically measuring current across a range of applied voltages, students plot a current-voltage ($V$-$I$) graph to verify Ohm's law and determine the wire's resistance.
Experimental Aim and Objectives
The primary objectives of this practical investigation are:
1. To assemble a DC test circuit incorporating a resistor, rheostat, DC power supply, series ammeter, and parallel voltmeter.
2. To measure the potential difference ($V$) across an unknown resistive conductor across a series of varying circuit current values ($I$).
3. To construct a linear current-voltage ($V$-$I$) graph from experimental data.
4. To verify that the ratio $V/I$ remains constant, confirming Ohm's law, and calculate the electrical resistance of the conductor from the slope of the graph.
Theoretical Background and Circuit Formulation
In 1827, Georg Simon Ohm demonstrated that the steady electric current flowing through a metallic conductor is directly proportional to the potential difference across its terminals, provided temperature and other physical conditions remain constant.
THEORETICAL V-I RELATIONSHIP
Voltage (V)
^
| / Line of Best Fit: Linear Slope
| .'
| .' Slope = Delta V / Delta I = Resistance (R)
| .'
| .'
| .'
|.'
0-------------------------------> Current (I)
Mathematical Formulation
Ohm's law is expressed mathematically as:
$$V \propto I \implies V = I R \implies R = \frac{V}{I}$$
Here: $V$ is the potential difference across the conductor, measured in volts ($\text{V}$). $I$ is the current traversing the conductor, measured in amperes ($\text{A}$). $R$ is the electrical resistance of the conductor, measured in ohms ($\Omega$).
If a metallic conductor satisfies Ohm's law, a plot of potential difference ($V$) on the vertical y-axis versus current ($I$) on the horizontal x-axis yields a straight line passing through the coordinate origin $(0,0)$. The slope of this line equals the conductor's resistance:
$$\text{Slope} = \frac{\Delta V}{\Delta I} = R$$
Circuit Diagram and Laboratory Apparatus
OHM'S LAW LABORATORY CIRCUIT
+-------( Battery / DC Supply )-------[/ ]-------+
| ( + - ) Key |
| |
| v
| [ Rheostat Rh ]
| [=== \ =======]
| |
| +----------[ Resistor R ]----------+ |
| | | |
| +--------------( V )---------------+ |
| Voltmeter |
| |
+----------------------( A )---------------------+
Ammeter
Apparatus Specifications
Regulated DC Power Supply (0 to 12 V variable, or a battery bank of four 1.5 V cells). Unknown Resistance Coil: A 1-meter coil of insulated Nichrome or Constantan wire wound on a wooden or ceramic spool. DC Ammeter: Range $0 \text{ to } 1.5 \text{ A}$ (with $0.05 \text{ A}$ minimum division). DC Voltmeter: Range $0 \text{ to } 3.0 \text{ V}$ (with $0.1 \text{ V}$ minimum division). Wire-Wound Rheostat: Range $0 \text{ to } 100\ \Omega$ (rated for $2 \text{ A}$). Plug Key (Single Pole Single Throw - SPST). Connecting Wires: Heavy-gauge insulated copper wires with alligator clips. Fine emery paper for terminal polishing.
Step-by-Step Experimental Procedure
- Clean the stripped ends of all connecting wires using emery paper to remove surface oxidation and ensure clean electrical contact.
- Determine the range and least count (minimum division) of both the ammeter and voltmeter. Check both meters for zero error with the circuit open; if a pointer deviates from zero, adjust the mechanical screw at the base of the needle.
- Assemble the circuit following the schematic diagram: Connect the positive terminal of the DC power supply to the single-pole plug key. From the key, connect to the lower fixed terminal of the rheostat. Connect the sliding contact terminal of the rheostat to the positive terminal of the ammeter. Connect the negative terminal of the ammeter to one end of the unknown resistor $R$. Connect the opposite end of resistor $R$ back to the negative terminal of the power supply. Finally, connect the voltmeter in parallel across resistor $R$, connecting the voltmeter's positive terminal to the incoming positive side and its negative terminal to the negative side.
- Position the sliding contact of the rheostat so that maximum resistance is included in the circuit, minimizing initial current.
- Insert the contact plug into the key to close the circuit.
- Adjust the rheostat slider until the ammeter registers a low readable current (for example, $0.20 \text{ A}$).
- Read and record the current ($I$) on the ammeter and the corresponding potential difference ($V$) on the voltmeter.
- Move the rheostat slider slightly to increase the current in increments (for example, $0.40 \text{ A}$, $0.60 \text{ A}$, $0.80 \text{ A}$, and $1.00 \text{ A}$). At each setting, record the ammeter and voltmeter readings in the observation table.
- Open the plug key after taking each reading to prevent continuous current flow, which would heat the resistor and alter its resistance.
- Calculate the ratio $R = V / I$ for each data pair, construct a $V$-$I$ graph, and determine the resistance from the line of best fit.
METER READING AND LEAST COUNT GUIDE
Ammeter Least Count = (Range) / (Total Divisions)
= 1.5 A / 30 divisions = 0.05 A/div
Voltmeter Least Count = 3.0 V / 30 divisions = 0.10 V/div
Observations and Experimental Results
EXPERIMENTAL DATA LOG: OHM'S LAW
Setting Current I (Amperes) Voltage V (Volts) R = V / I (Ohms)
------------------------------------------------------------------
1 0.20 A 0.60 V 3.00 Ohms
2 0.40 A 1.20 V 3.00 Ohms
3 0.60 A 1.80 V 3.00 Ohms
4 0.80 A 2.40 V 3.00 Ohms
5 1.00 A 3.00 V 3.00 Ohms
Data Processing and Graphical Calculations
Mean Calculated Resistance:
$$R_{\text{mean}} = \frac{3.00 + 3.00 + 3.00 + 3.00 + 3.00}{5} = 3.00\ \Omega$$
Determining Resistance from Graphical Slope: Plot potential difference ($V$) on the vertical y-axis and current ($I$) on the horizontal x-axis using the recorded data points. Draw the line of best fit through the plotted points and the origin. Select two coordinates along the line of best fit: $(I_1, V_1) = (0.30 \text{ A}, 0.90 \text{ V})$ and $(I_2, V_2) = (0.90 \text{ A}, 2.70 \text{ V})$. Calculate the slope:
$$\text{Slope} = \frac{\Delta V}{\Delta I} = \frac{V_2 - V_1}{I_2 - I_1} = \frac{2.70 \text{ V} - 0.90 \text{ V}}{0.90 \text{ A} - 0.30 \text{ A}} = \frac{1.80 \text{ V}}{0.60 \text{ A}} = 3.00\ \Omega$$
The straight line confirms that $V \propto I$, verifying Ohm's law. The resistance of the unknown conductor is determined to be $3.00\ \Omega$.
Laboratory Precautions and Sources of Error
- Joule Heating Effect: Passing high current continuously through the resistor generates thermal heat ($H = I^2 R t$). For metals, resistance increases with temperature. If the circuit is left closed, the resistance will drift upward, causing the $V$-$I$ curve to bend rather than form a straight line. Always remove the plug key between readings to allow the resistor to cool.
- Meter Polarities: Always connect the positive terminals of the ammeter and voltmeter toward the positive terminal of the power supply. Reversing polarities will deflect meter needles backward off-scale, risking damage to the delicate internal pointer suspensions.
- Meter Insertion Errors: An ammeter must always be connected in series with the component under test, while a voltmeter must be connected in parallel. Inserting an ammeter in parallel creates a short circuit that can burn out the meter coil, while inserting a voltmeter in series restricts circuit current to near zero due to its high internal resistance.
- Clean, Tight Connections: Loose connections or oxidized wire ends introduce stray contact resistances that distort readings. Tighten all binding posts securely.
Chapter Exercises and Solutions
Exercise 1: During an Ohm's law laboratory experiment, a student measures a potential difference of 2.40 volts across a Constantan wire coil while an ammeter registers a current of 0.80 amperes. If the applied potential difference is increased to 3.60 volts, calculate the new current flowing through the wire, assuming the temperature remains constant.
Solution 1: According to Ohm's law ($V = I R$), the electrical resistance of the Constantan wire is given by $R = V_1 / I_1 = 2.40 \text{ V} / 0.80 \text{ A} = 3.00\ \Omega$. Constantan is an alloy with a near-zero temperature coefficient of resistance, so its resistance remains constant. When the potential difference is increased to $V_2 = 3.60 \text{ V}$, the resulting current is $I_2 = V_2 / R = 3.60 \text{ V} / 3.00\ \Omega = 1.20 \text{ A}$. The new current traversing the wire is 1.20 amperes.
Exercise 2: Explain why a voltmeter must possess an extraordinarily high internal resistance and be connected in parallel, while an ammeter must possess an exceptionally low internal resistance and be connected in series within an Ohm's law test circuit.
Solution 2: An ammeter measures the rate of charge flow through a circuit branch. To record this flow accurately, the entire branch current must pass through the ammeter, requiring a series connection. If the ammeter possessed significant internal resistance, adding it would increase total circuit resistance and lower the current being measured. Therefore, ammeters are designed with near-zero internal resistance. A voltmeter measures the potential difference between two specific circuit nodes and must be connected in parallel across those points. If the voltmeter had low resistance, current would divert through the meter rather than the component, altering the circuit's operating voltages. Designing the voltmeter with high internal resistance ensures it draws negligible current, preserving the natural voltage across the component.
Exercise 3: A student performing an Ohm's law experiment leaves the plug key closed continuously while recording measurements. Over time, the calculated values of resistance ($R = V / I$) increase with each successive reading, and the resulting $V$-$I$ graph bends upward away from a straight line. Explain the physical mechanism causing this deviation.
Solution 3: Leaving the plug key closed allows current to flow through the resistor continuously, generating thermal energy via Joule heating ($H = I^2 R t$). As thermal energy accumulates, the temperature of the metallic wire rises. At higher temperatures, positive metal ions in the crystal lattice vibrate with greater amplitude around their equilibrium positions. These increased vibrations cause drifting conduction electrons to collide more frequently with the lattice, impeding electron flow. Consequently, the electrical resistance of the wire increases as it heats up. Because resistance is no longer constant, the ratio $V/I$ increases at higher current settings, causing the $V$-$I$ curve to bend upward away from a linear ohmic slope.