To use a resistance relationship, write R = V ÷ I, convert every quantity to volts, amperes or ohms, calculate, and state the answer with its unit. It appears whenever a question gives two of the three quantities and asks for the third.
This is the starting skill for the whole of potential difference, resistance and circuits. It builds on the idea of current from charge and current.
What does the relationship say?
Resistance is the potential difference needed for each ampere of current. If 1 V drives 1 A through a component, its resistance is 1 Ω.
| Quantity | Symbol | Unit |
|---|---|---|
| Potential difference | V | volt (V) |
| Current | I | ampere (A) |
| Resistance | R | ohm (Ω) |
The three forms are R = V ÷ I, V = I × R and I = V ÷ R. A larger resistance means less current for the same p.d.
How do I work through a question?
- List what is given with its unit, and write the unknown.
- Convert to base units: 1 mA = 0.001 A, 1 kΩ = 1000 Ω.
- Choose the form that has the unknown on its own.
- Substitute and calculate, keeping the units in the line.
- Check by multiplying back, and ask whether the size is sensible.
Worked example
A resistor has a p.d. of 9.0 V across it and carries a current of 250 mA. (Invented example data.) Find its resistance.
Step 1, convert: I = 250 ÷ 1000 = 0.250 A.
Step 2, choose: R = V ÷ I.
Step 3, calculate: R = 9.0 ÷ 0.250 = 36 Ω.
Step 4, check: I × R = 0.250 × 36 = 9.0 V, which matches the given p.d.
The answer is 36 Ω. A resistor of a few tens of ohms is a reasonable size for a school circuit.
The mistake to watch for
A common slip is to substitute the milliampere number directly.
Mistaken answer: R = 9.0 ÷ 250 = 0.036 Ω
The student used 250 as if it were in amperes. The equation only works in amperes, so the answer is 1000 times too small.
The correction is to convert first and to write the converted current on its own line. A quick size check also helps: 250 A would be an enormous current, so 250 must be in milliamperes.
Check yourself
Try these, then open each answer.
1. A heater element has 12 V across it and carries 3.0 A. Find its resistance.
Show answer
R = V ÷ I = 12 ÷ 3.0 = 4.0 Ω. Check: 3.0 × 4.0 = 12 V.
2. A 470 Ω resistor carries 20 mA. Find the p.d. across it.
Show answer
I = 20 ÷ 1000 = 0.020 A. V = I × R = 0.020 × 470 = 9.4 V. Check: 9.4 ÷ 470 = 0.020 A.
3. An 8.0 Ω resistor has 2.0 V across it. Find the current in amperes and in milliamperes.
Show answer
I = V ÷ R = 2.0 ÷ 8.0 = 0.25 A. In milliamperes, 0.25 × 1000 = 250 mA.
Where this leads next
Once the unit habit is automatic, move on to current in series and parallel branches, then test the whole topic with the circuit practice set. The circuit reasoning simulator lets you change a value and see the effect before you calculate.
Some students know each equation but still lose marks to units under time pressure. That is exactly the kind of pattern our teachers look for in online one-to-one Physics tuition.