Source: "Some Properties of Electric Circuits" lab (CCK simulation), Sections V–VI
Tags: Ohm's law, resistance, V=IR, current, voltage, variable resistor, inverse relationship, linear relationship, resistor, PHY-222, classical physics II
Difficulty: Intermediate | Prerequisites: Voltage fundamentals, series and parallel circuit behaviour (see earlier notes in this set).
The earlier parts of this lab showed qualitatively that adding bulbs changes brightness. This section makes those observations quantitative by introducing resistors with known values and measuring voltage and current directly. The result is Ohm's law, the single most used equation in circuit analysis. If you can confidently apply V = IR and recognise the shape of V-vs-I and I-vs-R graphs, you have the toolkit for nearly every DC-circuit problem in the course. You should already understand series and parallel wiring and be comfortable reading a voltmeter and ammeter.
When resistance is held constant, current rises in direct proportion to voltage (a straight-line graph). When voltage is held constant, current falls as an inverse function of resistance (a 1/R curve). Both observations are captured by one equation: V = IR.
Ohm's law
V = IR. The voltage across a resistive component equals the current through it multiplied by its resistance. In simple terms, if you push harder (more voltage) through the same obstacle (resistance), more charge flows per second (more current).
Resistance (R)
A measure of how strongly a component opposes the flow of current, measured in ohms (Ω). Higher resistance means less current for the same applied voltage.
Resistor
A circuit component designed to provide a specific, known resistance. Used to control current and divide voltage in a circuit.
Direct (linear) proportionality
Two quantities are directly proportional when doubling one doubles the other. The graph is a straight line through the origin. Voltage and current have this relationship when resistance is fixed.
Inverse proportionality
Two quantities are inversely proportional when doubling one halves the other. The graph is a hyperbola (1/x curve). Current and resistance have this relationship when voltage is fixed.
The circuit contains a single resistor at 10 Ω. The battery voltage is changed step by step and the current recorded.
Voltage (V) | Resistance (Ω) | Current (A) |
|---|---|---|
9 | 10 | 0.9 |
12 | 10 | 1.2 |
14 | 10 | 1.4 |
16 | 10 | 1.6 |
18 | 10 | 1.8 |
22 | 10 | 2.2 |
28 | 10 | 2.8 |
Current is strictly proportional to voltage: I = V / 10.
The graph of I versus V is a straight line through the origin with slope 1/R = 0.1 A/V.
Increasing the voltage provides a stronger "push" on the charges. Because the resistance (the opposition) stays the same, more charge flows per second, proportionally.
The battery stays at 9 V. The resistor value is changed from 10 Ω to 100 Ω.
Voltage (V) | Resistance (Ω) | Current (A) |
|---|---|---|
9 | 10 | 0.90 |
9 | 20 | 0.45 |
9 | 30 | 0.30 |
9 | 40 | 0.225 |
9 | 50 | 0.18 |
9 | 60 | 0.15 |
9 | 70 | 0.129 |
9 | 80 | 0.113 |
9 | 90 | 0.10 |
9 | 100 | 0.09 |
Current follows an inverse relationship with resistance: I = 9 / R.
The graph of I versus R is a hyperbola (a 1/x curve), not an exponential or polynomial. The curve drops steeply at first and then flattens, but never reaches zero.
Voltage across the resistor is constant at 9 V regardless of the resistance value, because the battery fixes it.
A light bulb is, electrically, just a resistor. Its filament has a resistance that determines how much current flows for a given voltage.
Adding bulbs in series is equivalent to increasing total resistance. The same Ohm's law relationship (V = IR) governs both the bulb experiments and the resistor experiments.
The only practical difference is that a bulb's resistance can change slightly with temperature, while the simulation's ideal resistors stay fixed.
Ohm's law
V = IR
Rearranged: I = V/R and R = V/I
Slope of the V-I graph (constant R)
slope = ΔV / ΔI = R
So the steeper the line, the higher the resistance.
Shape of the I-R graph (constant V)
I = V/R, which is a rectangular hyperbola. This is an inverse relationship, not an exponential one.
Power dissipated
P = IV = I²R = V²/R
Ohm's law is how electrical engineers size every wire, fuse, and resistor in a circuit. If you know the voltage supply and the resistance of a device, you can predict the current and choose a fuse that will blow before the current becomes dangerous. Dimmer switches in homes work by varying resistance: more resistance means less current through the bulb and lower brightness, exactly the pattern in Experiment 2.
The lab document calls the I-vs-R curve a "polynomial exponential relationship." This is incorrect. The relationship is an inverse proportion (I = V/R), which produces a hyperbolic curve. Be precise in your exam answers: call it inverse or 1/R, not exponential.
Students sometimes think that if you double the resistance, the current drops to zero. It halves; it does not disappear. Current only reaches zero at infinite resistance (an open circuit).
Some students confuse the V-I graph with the I-R graph. The V-I graph (constant R) is a straight line. The I-R graph (constant V) is a curve. They test different things.
A common error is applying Ohm's law to the battery itself as though the battery has no internal properties. In real life, batteries have internal resistance, which is why terminal voltage drops under heavy load. The simulation ignores this, so be aware of the simplification.
⚠️ Ohm's law (V = IR) will appear in some form on nearly every exam question involving DC circuits. Be able to rearrange it for any of the three variables.
⚠️ Know the shapes of both graphs: V vs. I is a straight line (slope = R); I vs. R is a 1/x hyperbola. You may be asked to sketch or interpret either one.
⚠️ Be ready to explain why current and voltage are directly proportional (for fixed R) and why current and resistance are inversely proportional (for fixed V). Examiners want the reasoning, not just the formula.
⚠️ The connection between bulbs and resistors is a favourite exam angle: "How is adding a bulb in series like increasing the resistance?"
Fill in the blank: V = ______.
True or false: Doubling the voltage across a fixed resistor doubles the current.
True or false: Doubling the resistance at fixed voltage doubles the current.
Fill in the blank: The graph of current vs. resistance at constant voltage is shaped like a ______.
True or false: A light bulb behaves as a source of resistance in a circuit.
Answers: 1. IR. 2. True. 3. False (it halves the current). 4. Hyperbola (1/x curve). 5. True.
Q: A 10 Ω resistor is connected to a 20 V battery. What current flows through the circuit?
A: I = V/R = 20/10 = 2 A.
Q: You plot current against voltage for a fixed resistor and get a straight line. The slope is 0.05 A/V. What is the resistance?
A: R = 1/slope = 1/0.05 = 20 Ω.
Q: With a 9 V battery, you increase resistance from 10 Ω to 30 Ω. By what factor does the current change?
A: Current drops by a factor of 3 (from 0.9 A to 0.3 A), because I = V/R and the resistance tripled while voltage stayed the same.
Q: A student says the I-vs-R graph is "exponential." Correct this and explain the actual relationship.
A: The relationship is inverse, not exponential. I = V/R describes a hyperbola: current falls as 1/R. An exponential decay (e.g. I = I₀ e^(−kR)) would approach zero much faster. The I-vs-R curve from Ohm's law has a long tail that flattens but never reaches zero for finite R.
Q: Explain why adding light bulbs in series produces the same electrical effect as increasing the resistance of a single resistor.
A: Each bulb has its own resistance. In series, resistances add (R_total = R₁ + R₂ + ...), so adding bulbs raises the total resistance of the circuit. A single resistor with the equivalent total value would produce identical voltage and current readings, because Ohm's law depends only on total resistance, not on how it is distributed.
Ohm's law feeds directly into Kirchhoff's loop and junction equations, which let you solve circuits with multiple loops and mixed series-parallel components. It also underpins the concept of equivalent resistance, which simplifies complex networks into a single-resistor model. Later in the course, Ohm's law extends to AC circuits, where impedance replaces simple resistance.
Ohm's law, V=IR, resistance, resistor, current, voltage, direct proportionality, inverse proportionality, hyperbola, V-I characteristic, I-R curve, variable resistor, power dissipation, equivalent resistance, internal resistance, PHY-222, classical physics II, CCK simulation, light bulb resistance