⚡ To find the current
Divide both sides of V = I × R by R.
I = V ÷ R
current = voltage ÷ resistance
Energy and Voltage in Circuits » Voltage, Current and Resistance
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 2.13
- The equation voltage = current × resistance, V = I × R, which you must learn
- What a resistance in ohms really tells you
- How to rearrange the equation to find the current or the resistance
- How to deal with mA and kΩ, and how to find a resistance from meter readings
🔒 Unlock Full Course Content
Sign up to access the complete lesson and track your progress!
Unlock This CourseFrom words to numbers
Remember, for the same applied voltage, more resistance means a smaller current. This lesson turns that rule into an equation, so that you can work out exactly how big the voltage, the current or the resistance is.
voltage = current × resistance
V = I × R
The spec says you must know and use this relationship. That means it is not given on the formulae page of the exam paper. You have to learn it by heart, in words and in symbols.
| Quantity | Symbol | Unit |
|---|---|---|
| Voltage | V | volt (V) |
| Current | I | ampere (A) |
| Resistance | R | ohm (Ω) |
Here V is the voltage across a component, I is the current in that component and R is the resistance of that component. All three must belong to the same component.
What a resistance in ohms tells you
The equation gives the ohm a clear meaning. The resistance of a component in ohms is the voltage needed across it for each ampere of current in it.
- A 5 Ω resistor needs 5 V across it to drive a current of 1 A.
- A 50 Ω resistor needs 50 V across it to drive the same 1 A.
- To drive 2 A through the 5 Ω resistor you need twice the voltage: 2 × 5 = 10 V.
So a high resistance means that a large voltage is needed to get even a small current. A low resistance means that a small voltage is enough to give a large current.
Worked example 1: finding the voltage
The current in a 15 Ω resistor is 0.4 A. Calculate the voltage across the resistor.
Equation: V = I × R
Substitution: V = 0.4 × 15
Answer: V = 6 V
Rearranging the equation
Exam questions do not always ask for the voltage. You need to be able to make the current or the resistance the subject.
🔌 To find the resistance
Divide both sides of V = I × R by I.
R = V ÷ I
resistance = voltage ÷ current
Notice that the voltage is always on top when you divide. If you find rearranging hard, draw a formula triangle: a triangle with V in the top section and I and R side by side in the bottom two sections. Cover the quantity you want. If the two that are left are side by side, multiply them. If one is above the other, divide the top one by the bottom one.
Worked example 2: finding the current
A 9 V battery is connected across a 45 Ω resistor. Calculate the current in the resistor.
Equation: V = I × R, so I = V ÷ R
Substitution: I = 9 ÷ 45
Answer: I = 0.2 A
Worked example 3: finding the resistance
An oil-filled radiator is plugged into the 230 V mains. The current in its heating element is 5 A. Calculate the resistance of the heating element.
Equation: V = I × R, so R = V ÷ I
Substitution: R = 230 ÷ 5
Answer: R = 46 Ω
Watch the units: mA and kΩ
The equation only works when the voltage is in volts, the current is in amperes and the resistance is in ohms. Small currents are often given in milliamperes (mA) and large resistances in kilohms (kΩ). Convert them before you put any numbers into the equation.
| Conversion | What to do | Example |
|---|---|---|
| mA to A | Divide by 1000 | 25 mA = 0.025 A |
| A to mA | Multiply by 1000 | 0.003 A = 3 mA |
| kΩ to Ω | Multiply by 1000 | 1.2 kΩ = 1200 Ω |
| Ω to kΩ | Divide by 1000 | 2000 Ω = 2 kΩ |
Worked example 4: a resistance in kΩ
There is a voltage of 6 V across a 2 kΩ resistor. Calculate the current in the resistor. Give your answer in mA.
Convert: R = 2 kΩ = 2 × 1000 = 2000 Ω
Equation: I = V ÷ R
Substitution: I = 6 ÷ 2000
Answer: I = 0.003 A
In milliamperes: 0.003 × 1000 = 3 mA
Worked example 5: mA and kΩ together
The current in a 1.2 kΩ resistor is 25 mA. Calculate the voltage across the resistor.
Convert: I = 25 mA = 25 ÷ 1000 = 0.025 A and R = 1.2 kΩ = 1200 Ω
Equation: V = I × R
Substitution: V = 0.025 × 1200
Answer: V = 30 V
Without the conversions you would get 25 × 1.2 = 30 by luck here, but only because the two factors of 1000 cancel. Convert only one of them and the answer is 1000 times out. Always convert both.
Finding a resistance from meter readings
You cannot read a resistance straight off a component the way you read a ruler. Instead you measure a voltage and a current, then calculate.
Picture the circuit. A battery, an ammeter and the component are joined in one loop, so the ammeter is in series with the component and measures the current in it. A voltmeter is then connected in parallel with the component, with one lead touching each end of it, so it measures the voltage across it.
Worked example 6: using meter readings
The voltmeter across a length of wire reads 4.5 V. The ammeter in series with the wire reads 0.18 A. Calculate the resistance of the wire.
Equation: R = V ÷ I
Substitution: R = 4.5 ÷ 0.18
Answer: R = 25 Ω
The spec suggests an optional investigation into the relationship between potential difference (voltage), current and resistance. It uses this same circuit: you take pairs of voltmeter and ammeter readings and use V = I × R to link them. You do not have to carry it out. The method is covered in the lesson Investigating Current and Voltage.
Common mistakes
- Dividing the wrong way up. Resistance is V ÷ I, never I ÷ V. Check that your answer is sensible: 230 V and 5 A cannot give a resistance of 0.02 Ω for a heater.
- Putting mA or kΩ straight into the equation. Convert to A and Ω first.
- Multiplying by 1000 when you should divide. A milliampere is small, so 25 mA must be a small number of amperes: 0.025 A.
- Mixing up I and 1. The symbol for current is the capital letter I.
- Leaving the unit off the answer, or writing the wrong one. Voltage in V, current in A, resistance in Ω.
- Using a voltage and a current that belong to different components. V, I and R must all be for the same component.
Exam-style question
A student connects a resistor, an ammeter and a power supply in a series circuit. A voltmeter measures the voltage across the resistor.
(a) State the equation linking voltage, current and resistance. [1 mark]
(b) Describe how the voltmeter should be connected to measure the voltage across the resistor. [1 mark]
(c) The voltmeter reads 7.5 V and the ammeter reads 0.25 A. Calculate the resistance of the resistor. Give the unit. [3 marks]
(d) The student replaces the resistor with a 1.5 kΩ resistor. The voltage across it is still 7.5 V. Calculate the current in this resistor. Give your answer in mA. [3 marks]
Model answer
(a) voltage = current × resistance, or V = I × R (1).
(b) In parallel with the resistor, with one lead connected to each end of it (1).
(c) R = V ÷ I = 7.5 ÷ 0.25 (1) = 30 (1) Ω (1).
(d) R = 1.5 kΩ = 1500 Ω (1). I = V ÷ R = 7.5 ÷ 1500 = 0.005 A (1) = 5 mA (1).
Exam tip
In part (d) there are two unit traps in one question: the resistance is given in kΩ and the answer is wanted in mA. Underline the units in the question before you start, convert 1.5 kΩ to 1500 Ω first, and only change your answer into mA at the very end.