Experiment 10: Ohm's Law and Resistance - Theory & Concepts

Experiment 10: Ohm's Law and Resistance

Learning Objectives

Define electric charge, electric current, conventional current, potential difference, electromotive force, resistance, conductance, resistivity, and electrical power.
Explain Ohm's law as a material and operating-condition relationship rather than a universal law for every device.
Relate resistance to conductor length, cross-sectional area, material resistivity, and temperature.
Interpret voltage-current and current-voltage graphs for ohmic and non-ohmic devices.
Calculate current, voltage, resistance, power, energy, and percentage difference using consistent SI units.
Explain the correct use and limitations of ammeters, voltmeters, and ohmmeters.
Use an interactive circuit simulation to predict changes before conducting the laboratory activity.

Ohm's law connects three fundamental circuit quantities: potential difference, electric current, and resistance. The equation is simple, but its correct interpretation requires an understanding of charge motion, energy transfer, material properties, temperature effects, measurement instruments, and the distinction between ohmic and non-ohmic behavior.

Target Learning Outcome

Explain the physical meaning and limitations of Ohm's law, determine resistance from calculations and graphs, and evaluate whether a device behaves approximately as an ohmic conductor.

1. Electric Charge and Current

Electric Charge

Electric charge is a fundamental property of matter responsible for electrical interactions. The SI unit is the coulomb, and the elementary charge magnitude is approximately $1.602\times10^{-19}\,\text{C}$ .

Electric Current

Electric current $I$ is the rate at which electric charge passes through a cross-section of a conductor.

Electric current

Current is charge flow per unit time.

I=\frac{\Delta Q}{\Delta t}

Variables

Symbol	Description	Unit
$I$	electric current	A
$\Delta Q$	charge passing a cross-section	C
$\Delta t$	elapsed time	s

Conventional Current

Conventional current is defined as the direction positive charge would move. In metallic conductors, electrons drift in the opposite direction.

Drift Velocity

Drift velocity is the small average directed velocity acquired by charge carriers in an electric field. It is much slower than the speed at which the electrical influence propagates through a circuit.

Current is not consumed

Charge is conserved. A resistor does not use up current; it transfers electrical energy into thermal energy while the same steady current enters and leaves the component. Current can divide only when the circuit contains branches.

2. Potential Difference and Energy

Electric Potential Difference

Potential difference or voltage $V$ is the change in electric potential energy per unit charge between two points.

Potential difference

Voltage measures energy transferred per coulomb of charge.

V=\frac{\Delta U}{q}

Variables

Symbol	Description	Unit
$V$	potential difference	V
$\Delta U$	change in electric potential energy	J
$q$	electric charge	C

Electromotive Force

Electromotive force or emf is the energy supplied by a source per unit charge. Despite its name, emf is a voltage rather than a mechanical force.

Energy interpretation of a resistor

A source gives charge electrical potential energy. As charge passes through a resistor, part of that energy becomes thermal energy. A voltage drop therefore represents energy transferred from the electrical system to another form.

3. Resistance, Conductance, and Resistivity

Electrical Resistance

Electrical resistance $R$ is the ratio of potential difference across a component to the current through it under specified conditions.

Conductance

Conductance $G$ measures how readily a component allows current. It is the reciprocal of resistance and is measured in siemens.

Resistance and conductance

Resistance opposes current, while conductance expresses ease of current flow.

R=\frac{V}{I}

G=\frac{1}{R}

Variables

Symbol	Description	Unit
$R$	electrical resistance	Ω
$G$	electrical conductance	S
$V$	potential difference	V
$I$	electric current	A

Resistivity

Resistivity $\rho$ is an intrinsic material property that measures opposition to current independent of the conductor's particular length and area.

Resistance of a uniform conductor

Resistance depends on material, length, and cross-sectional area.

R=\rho\frac{L}{A}

Variables

Symbol	Description	Unit
$\rho$	electrical resistivity	Ω·m
$L$	conductor length	m
$A$	cross-sectional area	$m^2$

Geometric and material effects

Doubling conductor length doubles resistance when material and area remain unchanged.
Doubling cross-sectional area halves resistance when material and length remain unchanged.
Low-resistivity materials are good conductors.
High-resistivity materials are useful as insulators or resistance elements.

4. Ohm's Law

Ohmic Conductor

An ohmic conductor is a device or material whose current is directly proportional to applied voltage over a specified operating range while physical conditions such as temperature remain approximately constant.

Ohm's law

For an ohmic conductor under constant physical conditions, voltage is proportional to current.

V=IR

Variables

Symbol	Description	Unit
$V$	potential difference across the conductor	V
$I$	current through the conductor	A
$R$	constant resistance over the tested range	Ω

What Ohm's law actually states

The equation $V=IR$ can always be used to define an instantaneous ratio $V/I$ , but a device obeys Ohm's law only when that ratio remains constant as voltage and current change. Constant temperature and an unchanged physical state are essential assumptions.

Cause-and-response interpretation

For a fixed resistance, increasing voltage increases current. For a fixed voltage, increasing resistance decreases current. The equation does not imply that voltage, current, and resistance are independent controls; changing one physical part of a real circuit can also change temperature and therefore resistance.

Interactive Ohm's law simulation

Change supply voltage and resistor values. Predict the equivalent resistance, total current, and power before moving each control. Compare series and parallel network behavior as preparation for Experiment 11.

Interactive engineering simulation

Ohm's Law Circuit Simulator

Switch between series and parallel resistance. Current, power, electron-flow speed, and bulb brightness update immediately.

Supply voltage12 V

1–48

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Resistance R16 Ω

1–50

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Resistance R24 Ω

1–50

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Governing Formulas

Ohm's Law

I = \frac{V}{R}

Equivalent Resistance (series)

R_{eq} = R_1 + R_2

Equivalent R

10.00 Ω

Current

1.20 A

Power

14.40 W

Model scope and verification

Use the displayed units and idealizations, then verify the governing balance or compatibility equation before interpreting the result.

5. Voltage-Current Characteristics

Current-Voltage Characteristic

A current-voltage characteristic is a graph showing how current through a device changes with the voltage across it.

Graph conventions and slope meaning

Graph	Vertical axis	Horizontal axis	Slope for an ohmic resistor
Voltage versus current	$V$	$I$	$R=\Delta V/\Delta I$
Current versus voltage	$I$	$V$	$G=\Delta I/\Delta V=1/R$

Identify the axes before using the slope

A common error is to call every straight-line slope resistance. The slope equals resistance only when voltage is plotted vertically and current horizontally. Reversing the axes makes the slope conductance.

Non-Ohmic Device

A non-ohmic device has a changing ratio $V/I$ over the tested range, so its current-voltage graph is nonlinear or has a changing slope.

Examples of non-ohmic behavior

An incandescent filament heats as current increases, raising its resistance.
A semiconductor diode conducts strongly in one direction only after sufficient forward bias.
A thermistor changes resistance significantly with temperature.
A light-dependent resistor changes resistance with illumination.

6. Temperature Dependence of Resistance

Temperature Coefficient of Resistance

The temperature coefficient $\alpha$ describes the fractional change in resistance per degree of temperature change near a reference temperature.

Linear temperature model for resistance

This approximation is useful over a limited temperature range.

R=R_0\left[1+\alpha\left(T-T_0\right)\right]

Variables

Symbol	Description	Unit
$R$	resistance at temperature T	Ω
$R_0$	resistance at reference temperature	Ω
$\alpha$	temperature coefficient of resistance	1/°C
$T$	final temperature	°C
$T_0$	reference temperature	°C

Positive and negative temperature coefficients

Most pure metals have positive temperature coefficients, so their resistance increases with temperature. Many semiconductor devices and thermistors can have negative coefficients over useful ranges, so their resistance decreases as temperature rises.

Self-heating during measurement

A resistor dissipates power and may warm during a high-current test. If temperature rises, the measured resistance can drift and the voltage-current graph may no longer represent constant-temperature behavior.

7. Electrical Power and Energy

Electrical Power

Electrical power $P$ is the rate at which electrical energy is transferred or converted.

Electrical power in a resistor

Equivalent forms follow from Ohm's law.

P=VI

P=I^2R

P=\frac{V^2}{R}

Variables

Symbol	Description	Unit
$P$	electrical power	W
$V$	potential difference	V
$I$	current	A
$R$	resistance	Ω

Electrical energy

Energy transferred equals power multiplied by elapsed time when power is constant.

E=Pt=VIt

Variables

Symbol	Description	Unit
$E$	electrical energy	J
$t$	elapsed time	s

Resistor power rating

A resistor must be operated below its rated power. Exceeding the rating can cause excessive temperature, resistance drift, discoloration, smoke, or component failure.

8. Resistor Values, Tolerance, and Color Codes

Nominal Resistance

Nominal resistance is the labeled or color-coded target value assigned by the manufacturer.

Tolerance

Tolerance is the permitted percentage difference between the actual resistance and the nominal value.

Tolerance range

The acceptable minimum and maximum values follow from the nominal value and tolerance fraction.

R_{\text{min}}=R_{\text{nom}}\left(1-\tau\right)

R_{\text{max}}=R_{\text{nom}}\left(1+\tau\right)

Variables

Symbol	Description	Unit
$R_{\text{nom}}$	nominal resistance	Ω
$\tau$	tolerance expressed as a decimal	dimensionless

Four-band resistor color code

Band	Meaning
First band	first significant digit
Second band	second significant digit
Third band	decimal multiplier
Fourth band	tolerance

Common tolerance colors include gold for $\pm5\%$ and silver for $\pm10\%$ .

9. Measuring Instruments and Circuit Loading

Ammeter

An ammeter measures current and is connected in series with the branch being tested. An ideal ammeter has zero resistance.

Voltmeter

A voltmeter measures potential difference and is connected in parallel across two points. An ideal voltmeter has infinite resistance.

Ohmmeter

An ohmmeter measures resistance using its own internal source and must be connected only to an isolated, de-energized component.

Real-meter effects

Real meters are not ideal. An ammeter has a small internal resistance that adds burden voltage to the circuit. A voltmeter has a large but finite resistance and draws a small current. These effects are usually minor in introductory work but can matter in high-resistance or low-voltage circuits.

Ammeter short-circuit hazard

Never place an ammeter directly across a source. Its low resistance can create a short circuit, excessive current, blown fuse, damaged meter, overheated wires, or damaged source.

Ohmmeter safety

Never measure resistance in an energized circuit. External voltage can produce false readings or damage the instrument.

10. Experimental Verification

Theory-guided Ohm's law investigation

STEP-BY-STEP

Identify the resistor nominal value, tolerance, and power rating.
Measure resistance with the circuit de-energized.
Connect the ammeter in series and voltmeter in parallel.
Begin with a low supply voltage and confirm correct polarity and meter range.
Record several voltage-current pairs while keeping resistor temperature approximately constant.
Plot $V$ versus $I$ and determine the best-fit slope.
Compare graph resistance, direct meter resistance, and nominal resistance.
Repeat with a non-ohmic device only when approved by the instructor.
Evaluate percentage difference and discuss uncertainty, tolerance, contact resistance, and heating.

Recommended data structure

Trial	Voltage $V$	Current $I$	Ratio $V/I$	Power $VI$	Observation
1
2
3
4
5

Percentage difference or error

Use the instructor's selected reference value consistently.

\%\,\text{difference}=\left|\frac{x_{\text{measured}}-x_{\text{reference}}}{x_{\text{reference}}}\right|\times100\%

Variables

Symbol	Description	Unit
$x_{\text{measured}}$	experimental value	varies
$x_{\text{reference}}$	accepted, nominal, or theoretical value	varies

Common sources of uncertainty

Resistor manufacturing tolerance
Meter calibration and resolution
Lead and contact resistance
Supply-voltage fluctuation
Ammeter burden voltage
Voltmeter loading
Temperature change from self-heating
Incorrect graph axes or slope calculation
Loose breadboard connections
Unit conversion errors between amperes and milliamperes

Engineering applications

Ohm's law and resistance concepts are used in sensor circuits, instrumentation, power distribution, building electrical systems, control panels, electronic devices, heating elements, fault analysis, and equipment protection. Engineers must combine the ideal equations with power ratings, tolerances, thermal behavior, and measurement limitations.

Key Takeaways

Current is the rate of charge flow, while voltage is energy transferred per unit charge.
Resistance depends on material resistivity, conductor length, cross-sectional area, and temperature.
An ohmic conductor has an approximately constant ratio $V/I$ under constant physical conditions.
The slope of a $V$ -versus- $I$ graph is resistance; the slope of an $I$ -versus- $V$ graph is conductance.
Non-ohmic devices have changing resistance or nonlinear voltage-current behavior.
Electrical power can be calculated from $P=VI$ , $P=I^2R$ , or $P=V^2/R$ .
Resistor tolerance and power rating are essential practical limits.
Ammeters connect in series, voltmeters connect in parallel, and ohmmeters require a de-energized component.
Simulation should be used to predict trends before physical measurement.
Experimental disagreement should be explained using tolerance, instrument effects, contact resistance, temperature, and uncertainty.

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