Current, resistance and potential difference
The relationship between current ($I$), potential difference ($V$) and resistance ($R$) underpins every circuit calculation in GCSE Physics.
The key equation
$V = IR$
- $V$ — potential difference, in volts (V).
- $I$ — current, in amperes A.
- $R$ — resistance, in ohms (Ω).
Rearranged: $R = V/I$ and $I = V/R$.
What is potential difference?
Potential difference (p.d., or voltage) between two points is the energy transferred per unit charge as the charge moves between them. 1 V = 1 J/C. A 12 V battery transfers 12 J of energy to every coulomb of charge that passes through it.
What is resistance?
Resistance is how hard it is for current to flow through a component. A high resistance means a small current for a given p.d. Resistance arises because charge carriers (electrons) collide with vibrating ions in the lattice.
Ohm's law
For an ohmic conductor at constant temperature, the current through it is directly proportional to the p.d. across it. So $V/I$ is constant — i.e. the resistance is constant. The IV graph is a straight line through the origin.
✦Worked example— Worked example 1
A 6.0 V battery drives 0.20 A through a resistor. Find the resistance.
- $R = V/I = 6.0 / 0.20 = 30$ Ω.
✦Worked example— Worked example 2
A 12 Ω resistor is connected to a 9.0 V supply. Find the current.
- $I = V/R = 9.0 / 12 = 0.75$ A.
Required practical 3 — IV characteristics
A standard piece of apparatus: a battery, ammeter (in series), variable resistor, voltmeter (in parallel with the test component).
- Vary the variable resistor to get a range of currents.
- For each setting, record $I$ and $V$.
- Reverse the cell to obtain negative values.
- Plot $I$ (y) against $V$ (x).
For an ohmic resistor at constant temperature: a straight line through the origin (positive and negative quadrants).
⚠Common mistakes
- Forgetting to convert mA to A or kΩ to Ω before substituting.
- Putting an ammeter in parallel — short-circuits the component.
- Treating non-ohmic components like ohmic ones — a filament lamp does NOT have constant resistance because it heats up.
- Saying "voltage flows" — voltage is not a flow; current flows. Voltage is the cause.
➜Try this— Quick check
A 4.5 V cell pushes 0.30 A through a resistor. Find $R$.
- $R = V/I = 4.5 / 0.30 = 15$ Ω.
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