D. Physics: Principles and Applications of Electricity · Electricity: Charges, Circuits and Energy

Applying Ohm's Law to Real-World Problems

D2.5 A2.4About 65 minutes

Learning goals

I can rearrange V = I × R to find any one of the three quantities.
I can convert between mA and A, and between Ω, kΩ and MΩ, before calculating.
I can solve real-world problems with Ohm's law using a clear method (GRASS).
I can use Ohm's law to explain electrical safety, such as why wet skin is dangerous.

Words to know

Ohm's law
V = I × R. Potential difference (volts) equals current (amperes) times resistance (ohms).

GRASS
A problem-solving method: Given, Required, Analysis (formula), Solution (with units), Statement (answer in a sentence).

milliampere (mA)
One thousandth of an ampere. 1 A = 1000 mA.

kilohm (kΩ)
One thousand ohms. 1 kΩ = 1000 Ω. A megohm (MΩ) is one million ohms.

rated current
The current a device or fuse is designed to carry, printed on its label.

From the lab to real life

You built a mathematical model: V = I × R. Now you will put it to work. Electricians use it to choose wires and breakers, engineers use it to design phone chargers, and you can use it to understand why a kettle needs a thick cord and why wet hands and electricity never mix.

The Ohm's law triangle. Cover the quantity you want: what is left shows how to calculate it. V over I means divide; I beside R means multiply.

A clear method: GRASS

Given: list the known values with units. Convert to base units (A, V, Ω).
Required: what are you finding?
Analysis: write the formula, rearranged for the unknown.
Solution: substitute, with units, and calculate.
Statement: answer in a sentence with the right number of digits and the unit.

Converting units. Going from a smaller unit to a larger one, divide by 1000; going from larger to smaller, multiply by 1000. For example 250 mA = 0.250 A and 4.7 kΩ = 4700 Ω.

The flashlight in Example 1 (below) as a circuit diagram: a 3.0 V battery, a closed switch, an ammeter and a 6.0 Ω lamp in one loop.

Worked example

Example 1: A flashlight (find I)

A flashlight uses a 3.0 V battery and a lamp with a resistance of 6.0 Ω. What will the ammeter read?

G: V = 3.0 V, R = 6.0 Ω
R: I = ?
A: I = V ÷ R
S: I = 3.0 V ÷ 6.0 Ω = 0.50 A

S: The current through the lamp is 0.50 A (500 mA).

Worked example

Example 2: An electric kettle (find R)

A kettle plugged into a 120 V outlet draws a current of 12.5 A. What is the resistance of its heating element?

G: V = 120 V, I = 12.5 A
R: R = ?
A: R = V ÷ I
S: R = 120 V ÷ 12.5 A = 9.6 Ω

S: The heating element has a resistance of 9.6 Ω. A low resistance at 120 V means a large current, which is why kettles need heavy cords.

Worked example

Example 3: A sensor (find V, with conversions)

A sensor in a smart thermostat has a resistance of 2.2 kΩ and carries a current of 1.5 mA. What is the potential difference across it?

G: R = 2.2 kΩ = 2200 Ω; I = 1.5 mA = 0.0015 A
R: V = ?
A: V = I × R
S: V = 0.0015 A × 2200 Ω = 3.3 V

S: The potential difference across the sensor is 3.3 V.

Ohm's law and safety

Your body has resistance too. It changes a lot from person to person and from moment to moment. As a rough idea, dry skin might have a resistance of about 100 000 Ω, while wet skin might be closer to 1000 Ω.

At 120 V:

Dry: I = 120 V ÷ 100 000 Ω = 0.0012 A (1.2 mA)
Wet: I = 120 V ÷ 1000 Ω = 0.12 A (120 mA), 100 times more.

A current that large through the body can stop the heart. That is why bathrooms and kitchens near sinks use special GFCI outlets (ground fault circuit interrupters, with "Test" and "Reset" buttons), which shut off the power within a fraction of a second if current starts leaking where it should not.

Worked example

Example 4: Choosing a fuse

A car's rear-window defroster has a resistance of 1.2 Ω and runs on the car's 12 V battery. Fuses come in 5 A, 10 A, 15 A and 20 A ratings. Which fuse should be used?

I = V ÷ R = 12 V ÷ 1.2 Ω = 10 A.
The fuse must let the normal current through without melting, so it must be rated above 10 A.
It should still be as low as possible, so it blows quickly if there is a fault.

Use the 15 A fuse: the smallest rating above the normal 10 A current. (In a real car, always use the fuse rating printed in the owner's manual.)

Watch out!

Convert mA to A and kΩ to Ω before using V = I × R.
Check your answer makes sense: more resistance should give less current.
Keep sensible significant digits: if the data have 2 digits, give 2 or 3 digits in the answer.

Hands-on activity

Appliance label survey

You need: 3 or 4 unplugged heating appliances (kettle, toaster, hair dryer, space heater), a notebook, a calculator.

Find each label. Record the voltage (in Canada usually 120 V) and the current in amperes (A), if it is given.
Calculate the resistance of each heating element: R = V ÷ I.
Rank the appliances from lowest to highest resistance. Which draws the most current?
Look at each power cord. Is there a link between the current and the thickness of the cord?

Model answer: a label reading "120 V ~ 60 Hz 12.5 A" gives R = 120 ÷ 12.5 = 9.6 Ω. Appliances with lower resistance draw more current and usually have thicker cords. If a label lists only watts (W), save it for the lesson on electrical energy, where you will learn to use power.

Safety (grown-up note): Make sure every appliance is unplugged and cool before handling it. Only read the labels; do not open anything. (For motors, such as in a fan, V ÷ I is not a simple resistance, so stick to heating appliances.)

Just for fun

Why does V always sit at the top of the Ohm's law triangle?

Because it has the most potential.

Your turn

A 9.0 V battery is connected to a 45 Ω resistor. What is the current?

A current of 2.5 A flows through a 48 Ω heater. What is the potential difference across it?

A toaster draws 10 A from a 120 V outlet. What is its resistance?

Convert: (a) 750 mA to A, (b) 3.3 kΩ to Ω.

A 6.0 V battery is connected to a 1.5 kΩ resistor. Find the current in mA.

Use Ohm's law to explain why touching a switch with wet hands is more dangerous than with dry hands.

More practice: warm-up

V = 12 V, R = 4.0 Ω. Find I.

I = 0.50 A, R = 10 Ω. Find V.

V = 6.0 V, I = 2.0 A. Find R.

Convert 0.025 A to mA.

What does the first S in GRASS stand for?

More practice: on your own

A phone charger supplies 5.0 V. The phone's charging circuit acts like a 2.5 Ω load. What current flows?

An LED string light has a resistance of 480 Ω when lit and runs on 120 V. What is the current in mA?

A multimeter shows 18 mA through a resistor with 3.6 V across it. What is the resistance in kΩ?

A space heater has a resistance of 9.6 Ω on a 120 V circuit protected by a 15 A breaker. Will the breaker trip if only the heater is on? Explain.

A student calculates the current through a 220 Ω resistor at 5.0 V and gets 1100 A. What mistake did they make? What is the right answer?

Challenge

On the same 120 V circuit (15 A breaker), someone runs the 9.6 Ω space heater and also turns on a 12 Ω toaster. Each draws its own current from the outlet, and the currents add. Will the breaker trip?

A resistor's colour code says 330 Ω. When you put 9.0 V across it, you measure 25 mA. Is the resistor within a 5% tolerance of its label?

A worker accidentally touches a 600 V line. Estimate the current if their body resistance is 100 000 Ω, and again if it is 2000 Ω (sweaty). Why do electrical workers wear insulated gloves?

Check your understanding

Quiz

A 12 V battery is connected to a 3.0 Ω lamp. The current is:

Which equation gives resistance?

What is 40 mA in amperes?

A heater draws 8.0 A at 120 V. Its resistance is:

Why is electricity more dangerous with wet hands?

A 2.0 kΩ resistor carries 3.0 mA. What is the potential difference across it?

For parents and teachers

Big idea: Expectation D2.5 asks students to apply the mathematical model (Ohm's law) to calculate current, potential difference and resistance in real-world situations. Linking calculations to home safety connects to A2.4 (scientific literacy about everyday issues).

Common difficulties:

Rearranging the formula. The triangle helps, but encourage algebra too (divide both sides by I).
Prefixes. Most wrong answers come from not converting mA and kΩ.
Unreasonable answers (1100 A from a 5 V battery!). Teach your teen to ask, "Does this make sense?"

How to help: Read appliance labels together (unplugged and cool), and talk about why kitchens and bathrooms have GFCI outlets. Body resistance values in this lesson are rough estimates that vary widely; the key idea is that wet skin conducts far better than dry skin.