Connect one, two, then three cells to the same nichrome wire, and as the voltage rises the ammeter reading follows at one, two and three times. Voltage and current are proportional, and their ratio is the resistance: that is Ohm's law, V = IR.
The first graph plots those measurements. With voltage up the side and current along the bottom, the slope of the line through the origin is the resistance, and a larger resistance gives a steeper line.
The second diagram shows how to connect the meters for such an experiment: the ammeter in line with the circuit, the voltmeter across the ends of the resistor being measured.
A voltmeter connected across a plain wire reads almost 0 V, so it must go across the very part you want to measure.
How Voltage, Current and Resistance Relate
🚿 Seen as Flowing Water
①Voltage (V) is like water pressure: the higher it is, the harder the water flows
②Current (I) is like the amount of water flowing each second
③Resistance (R) is like a narrow pipe: the narrower it is, the less water flows
④So current is proportional to voltage and inversely proportional to resistance
Ohm's Law on a Graph
seegongsik.com
Graph with current across and voltage up, showing that the slope of the line is the resistance
6V
3Ω
💡 Current now flowing: 2.0 A
①With voltage up and current across, the slope of the line (V ÷ I) is the resistance
②The dashed lines are 2 Ω and 5 Ω; the larger the resistance, the steeper the line
③Raising the voltage moves the point up the same line and increases the current
④Changing the resistance changes the slope of the line itself
Connecting an Ammeter and a Voltmeter
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Circuit with the ammeter in series and the voltmeter in parallel across the resistor
Connecting an ammeter
Ammeter → in series with the circuit (very low internal resistance)
All the current being measured has to pass through it, so it goes in line with the circuit
Connecting a voltmeter
Voltmeter → in parallel across the part measured (very high internal resistance)
It measures the voltage difference between two points, so it goes across the ends of the part being measured
Three Forms of Ohm's Law
Ohm's law
V = I × R
Voltage (V) = current (A) × resistance (Ω)
Finding current
I = VR
Current (A) = voltage (V) ÷ resistance (Ω)
Finding resistance
R = VI
Resistance (Ω) = voltage (V) ÷ current (A). It can also be read as the slope of a voltage-current graph
Summary
Ohm's law
V = IR
Knowing any two of voltage, current and resistance gives the third
🎯 Common Test Points
①With fixed resistance, doubling the voltage doubles the current
②With fixed voltage, doubling the resistance halves the current
③On a graph with V up and I across, a steeper slope means a larger resistance (swapping the axes reverses this)
④An ammeter goes in series, a voltmeter in parallel
⑤For conductors that heat up a lot, such as a bulb filament, the graph bends away from a straight line
Examples and Unit Review
Example 1
What current flows through a 4 Ω nichrome wire when 12 V is applied across it?
1
From Ohm's law V = IR, the current is I = V ÷ R.
2
I = 12 V ÷ 4 Ω = 3 A.
▸ 3 A
With 6 V across the same wire the current halves to 1.5 A: with the resistance unchanged, current is proportional to voltage.
Example 2
How are an ammeter, which measures current, and a voltmeter, which measures voltage, connected in a circuit?
1
An ammeter goes in line (in series) with the circuit so that all the current being measured passes through it.
2
A voltmeter measures the voltage between two points, so it goes across the ends (in parallel) of the part being measured.
▸ The ammeter in series, the voltmeter in parallel
Connecting an ammeter in parallel is risky: its low internal resistance lets a large current through, which can damage it.
Unit-test style
Which statement about Ohm law is correct?
①At constant voltage, a larger resistance gives a larger current
②Ohm law is expressed as V = IR
③An ammeter is connected in parallel in a circuit
④At the same resistance, raising the voltage decreases the current
⑤On a V-I graph, the slope represents the voltage
▸ ② Ohm law is expressed as V = IR
1
Ohm law is voltage = current × resistance, that is V = IR.
2
A larger resistance gives a smaller current (①), an ammeter is connected in series (③), raising the voltage increases the current (④), and the slope of a V-I graph represents the resistance (⑤).