Ohm's law
Current through a wire grows in step with the potential difference.
Twice the push
A metallic wire is joined to a cell and a steady current flows in it. The temperature of the wire stays the same. The cell is then replaced by one that gives twice the potential difference.
What happens to the current in the wire?
What this lesson covers
The idea
The potential difference V across a metallic wire is directly proportional to the current I through it at constant temperature: V = IR, a straight-line V–I graph through the origin; hence I = V/R: current is inversely proportional to resistance.
Twice the push
A metallic wire is joined to a cell and a steady current flows in it. The temperature of the wire stays the same. The cell is then replaced by one that gives twice the potential difference.
What happens to the current in the wire?
- It becomes twice as large
- It stays the same
- It becomes half as large
V and I
Change V and the wire. Watch the red point on the graph of V against I.
A straight line
The red point always sat on a straight line through the origin: when V doubled, I doubled. A wire with a bigger resistance R gave a smaller current for the same V, so its line leaned the other way.
The potential difference V across a metallic wire is directly proportional to the current I through it, provided its temperature is constant: V = IR. The graph of V against I is a straight line through the origin. Hence I = V/R: the current is inversely proportional to the resistance.
Notes
V = IR for a metallic wire at constant temperature: V is directly proportional to I, the graph of V against I is a straight line through the origin, and I = V/R, so I is inversely proportional to R.
Check yourself
A wire carries 2 A when the potential difference across it is 6 V. What current flows when the potential difference is 12 V and the temperature is the same, in A?
Answer: 4 A
V is directly proportional to I, so doubling V from 6 V to 12 V doubles the current from 2 A to 4 A.
What does the graph of V against I of a metallic wire at constant temperature look like?
The resistance in a circuit is doubled while the potential difference stays the same. What happens to the current?
The potential difference across a heater is 60 V when it draws 4 A. What is its resistance, in Ω?
Answer: 15 Ω
R = V/I = 60 V divided by 4 A = 15 Ω.
- A curve that bends upwards. For a metallic wire at constant temperature the ratio V/I is constant, which gives a straight line.
- A straight line that starts above the origin on the V axis. When V is zero the current is zero, so the line passes through the origin.
- A straight line through the origin — correct. Yes!
- It becomes half — correct. Yes!
- It becomes double. Current is inversely proportional to resistance, so doubling the resistance halves the current.
- It stays the same. I = V/R, so with the same V a different R changes I.