Lesson 4 of 8Principles & Applications of Electricity

Unit 4 · Lesson 4 of 8

Ohm's Law

For many conductors, the current is directly proportional to the potential difference across them, and the ratio of the two is the resistance. That relationship, Ohm's law, is written V = IR. Learn to rearrange it, use it with real numbers and units, read a graph of V against I, and apply it to real situations like heaters, short circuits and wet skin.

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Key things to remember

1Ohm's law: $V = I R$ , so $I = \frac{V}{R}$ and $R = \frac{V}{I}$ .
2Use volts, amperes and ohms: 1000 mA = 1 A and 1 k $Ω$ = 1000 $Ω$ .
3For an ohmic resistor, current is directly proportional to potential difference: double V, double I.
4On a graph of V (vertical) against I (horizontal), the slope is the resistance; a steeper line means more resistance.
5Lamps, LEDs and diodes are non-ohmic: their resistance changes as the current changes.

Turn up a dimmer switch and the light gets brighter. Plug a toaster into a 120 V outlet and it draws about 10 A, while a phone charger draws a tiny fraction of that. Why? In the 1820s the German scientist Georg Ohm tested wires of different lengths and thicknesses and found a simple pattern connecting three quantities you already know: potential difference, current and resistance. His pattern lets you predict the current in a circuit before you even switch it on.

The relationship

For many conductors kept at a steady temperature, if you double the potential difference across them, the current doubles; triple it and the current triples. Current is directly proportional to potential difference. The ratio $\frac{V}{I}$ stays the same, and that constant ratio is the resistance. Writing it as an equation gives Ohm's law. It also makes sense: a bigger push (more volts) drives more current, while more resistance lets less current through for the same push.

V = I R I = \frac{V}{R} R = \frac{V}{I}

V in volts (V), I in amperes (A), R in ohms (Ω). All three are the same law, rearranged.

Fig 1Cover the quantity you want in the V-over-I-R triangle: V = IR, I = V/R and R = V/I. The second triangle is for power, P = VI, which you will use in the lesson on energy and power; the other power formulas shown are for later physics courses.

Get the units right first

Ohm's law only works directly in volts, amperes and ohms. Change milliamperes to amperes by dividing by 1000 (25 mA = 0.025 A). Change kilohms to ohms by multiplying by 1000 (2.2 k

Ω

= 2200

Ω

Graphing potential difference against current

In a lab you can set different voltages, measure the current each time, and plot V on the vertical axis against I on the horizontal axis. For a resistor that obeys Ohm's law, the points fall on a straight line through the origin. The slope of that line is $\frac{rise}{run} = \frac{Δ V}{Δ I}$ , which is exactly the resistance. A steeper line means a larger resistance, because it takes more volts to push the same current.

Current I (A)	Potential difference V (V)	V ÷ I (Ω)
0.10	2.0	20
0.20	4.0	20
0.30	6.0	20
0.40	8.0	20

Data for one resistor. Doubling the current needs double the voltage, and V ÷ I is always 20 Ω, so the graph is a straight line with slope 20 Ω.

Not every device behaves this way. A lamp's thin filament heats up as more current flows, and hotter metal has more resistance, so its V against I graph curves. LEDs and diodes do not follow the pattern either. Devices that follow Ohm's law are called ohmic; those that do not are non-ohmic. For a non-ohmic device you can still calculate $R = \frac{V}{I}$ at one particular moment, but that value changes as the current changes.

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Series and parallel circuit simulator. Stay in series mode and slide the supply voltage: the total current rises in step with the voltage, exactly as I = V/R predicts. Then raise a resistance and watch the current drop.

Ohm's law in the real world

Heaters and toasters have a fairly low resistance so that a large current flows and lots of electrical energy becomes thermal energy. A 12 $Ω$ toaster element on a 120 V outlet draws $120 \div 12 = 10$ A.
Dimmers and volume knobs often use a variable resistor: turning the knob changes the resistance, which changes the current.
Wet skin is dangerous because water lowers your body's resistance. As rough example values, dry skin might have a resistance near 100 000 $Ω$ and wet skin near 1000 $Ω$ . At 120 V that is the difference between about 0.0012 A and 0.12 A, and a current of about 0.1 A through the chest can stop the heart.
Short circuits happen when current finds a path with almost no resistance, such as two bare wires touching. With R nearly zero, $I = V / R$ becomes huge, wires overheat and fires can start. Fuses and circuit breakers open the circuit when the current gets too high.

Career connection: electrical engineer

Electrical engineers use Ohm's law every day to choose wire sizes, resistors and protective devices so that circuits carry the current they need without overheating. In Ontario, becoming a professional engineer usually means a university engineering degree followed by supervised work experience and a licence from Professional Engineers Ontario.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1

A flashlight bulb has a potential difference of 3.0 V across it and a current of 0.50 A through it. What is its resistance?

Example 2

A toaster element has a resistance of 12

Ω

and is plugged into a 120 V outlet. What current does it draw?

Example 3

A current of 25 mA flows through a 220

Ω

resistor. What is the potential difference across the resistor?

Example 4

A graph of potential difference (vertical axis) against current (horizontal axis) for a resistor is a straight line through the origin and the point (0.40 A, 8.0 V). Find the resistance.

Where marks get lost

Plugging milliamperes straight into V = IR. Convert to amperes first (divide by 1000), or the answer is 1000 times off.
Rearranging wrongly, for example writing I = R/V. Use the triangle: V on top, so I = V/R and R = V/I.
Thinking that raising the voltage raises a resistor's resistance. For an ohmic resistor, R stays the same; the current goes up instead.
Reading the slope of an I against V graph (current on the vertical axis) as the resistance. On that graph the slope is 1/R; only on a V against I graph is the slope R. Check which quantity is on each axis.
Assuming every device obeys Ohm's law. A lamp filament's resistance rises as it heats up, so its graph curves.

Flashcards 8

Ohm's law

Find current

Find resistance

Slope of a V against I graph

+ 4 more

Practice

A 12 V battery is connected to a 4.0

Ω

resistor. What current flows, in amperes?

A current of 0.20 A flows through a 45

Ω

resistor. What is the potential difference across it, in volts?

A kettle draws 8.0 A from a 120 V outlet. What is the resistance of its heating element, in ohms?

A 6.0 V source is connected across a 300

Ω

resistor. What is the current in milliamperes (mA)?

The potential difference across an ohmic resistor is doubled. What happens to the current through it?

Two resistors are tested and their results plotted on the same V (vertical) against I (horizontal) graph. Line A is steeper than line B. What does this tell you?

A straight line on a V (vertical) against I (horizontal) graph passes through the origin and the point (0.25 A, 5.0 V). What is the resistance, in ohms?

Match what you need to find with the form of Ohm's law to use.

Potential difference

Current

Resistance

What is the SI unit of resistance? Give the name of the unit.

As a rough example, a person with wet hands might have a body resistance of about 1000

Ω

. What current would 120 V push through them, in milliamperes?

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