Electric Circuits · Grade 10
What decides how much current goes through a component?
The voltage across it and its resistance. Ohm's law says the current equals the voltage divided by the resistance, so the same voltage drives a larger current through a smaller resistor. On a graph of voltage against current an ordinary resistor gives a straight line, and the resistance is that line's gradient.
Learning objectives
- Calculate the current through a resistor given the voltage across it and its resistance
- Plot voltage against current for a resistor and get the resistance from the slope of the line
- Predict how the resistance of a wire changes when it is made longer, thicker or hotter
- Explain why a filament lamp does not give a straight line on a voltage against current graph
The law and what it says
Current equals voltage divided by resistance. It can be rearranged into any form — voltage equals current times resistance, resistance equals voltage divided by current — and it is the same relation.
Resistance is measured in ohms. One ohm is the resistance in which one volt drives one ampere.
It is worth knowing that Ohm's law is not a universal law of nature but a description of a particular behaviour. Materials that follow it are called ohmic, and not every component is.
The graph
Plot voltage on one axis and current on the other and take several readings. For an ordinary resistor at a constant temperature the result is a straight line through the origin.
The gradient gives the resistance: voltage divided by current. So a steeper line means a larger resistance, and the number can be read from any two points on it.
A filament lamp does not give a straight line but a curve that flattens. The reason is physical: the current heats the filament, and the resistance of a metal rises with temperature. The lamp changes its own resistance during the measurement.
What changes a wire's resistance
Length: a longer wire resists more, in direct proportion. Twice the length, twice the resistance.
Thickness: a thicker wire resists less, in inverse proportion to its cross-sectional area. The right picture is a pipe — long and narrow is hard, short and wide is easy.
Temperature: in metals resistance rises with heat, because the atoms vibrate harder and get in the way more. The material itself matters too, which is why mains wiring is copper and not steel.
Worked examples
A 20 ohm resistor has 10 V across it. What is the current?
- Current equals voltage divided by resistance
- 10 divided by 20
Answer: 0.5 amperes
On a voltage-current graph for a resistor, one point is 6 V and 1.5 A. What is the resistance?
- The resistance is the gradient, voltage divided by current
- 6 divided by 1.5
Answer: 4 ohms
A wire is replaced by one of the same material, twice as long and twice the cross-sectional area. What happened to its resistance?
- Twice the length doubles the resistance
- Twice the area halves it
- The two changes cancel
Answer: The resistance is unchanged
Common mistakes
- Expecting every component to give a straight line
- Only an ohmic component at a constant temperature does. A filament lamp heats up during the measurement, its resistance rises, and the graph curves.
- Calculating the gradient as current over voltage
- Resistance is voltage over current. Inverting it gives the conductance, and a number like 0.25 instead of 4 gives the slip away at once.
- Thinking a thicker wire resists more
- Thicker means more room to get through, so less resistance. It is why a cable carrying a large current is made thick.
What to remember
- Current equals voltage over resistance.
- On a voltage-current graph, resistance is the gradient.
- Longer resists more; thicker resists less.
- A filament lamp is not ohmic — it heats up.