Voltage is a difference in energy, and current is the flow of electric charge.
Voltage is the difference in electrical energy per unit of charge, and 1 V represents 1 J/C. Current is the amount of charge passing through a cross-sectional area in a unit of time, and 1 A represents 1 C/s. Voltage indicates the condition for energy transfer, while current represents the actual amount of charge movement.
In an ideal resistance, V = IR, we can change it to I = V/R. If we double the voltage, then with the same resistance, the current also doubles. If we double the resistance, then with the same voltage, the current becomes half. The key is what we keep constant in each comparison.
When reading a graph’s slope, first verify the axes.
If the horizontal axis represents voltage V and the vertical axis represents current I, the graph is I = (1/R)V, and therefore the slope is 1/R. As the resistance increases, the line becomes flatter. If the horizontal axis represents current and the vertical axis represents voltage, the graph is V = RI, and therefore the slope is R. As the resistance increases, the line becomes steeper.
To check whether a graph is linear, measure at several voltages rather than calculating V/I at only one point. With a constant offset or measurement error, also check whether the graph passes through the origin and how far it deviates from proportionality.
Measurement circuit and conditions of validity
The ammeter is connected in series with the resistor being measured, and the voltmeter is connected in parallel across both ends of the resistor. An ideal ammeter resistor is close to 0, and the voltmeter’s resistance is very large, minimizing its impact on the circuit. In the experiment, the circuit is completed, the switch is closed, and the values are recorded.
Ohm's law is not a universal linear law for all electronic components. Diodes, light bulbs whose brightness changes with temperature, and non-ohmic resistors do not exhibit a simple proportional relationship between voltage and current. The resistance measured in experiments excludes temperature variations and the internal resistance of the power source and instruments.
Key relationships and symbols
V = IR · I = V/R · P = VI
| Symbol | Meaning | Unit |
|---|---|---|
| V | Voltage across the resistor | V |
| I | Current through the resistor | A |
| R | Resistance | Ω |
| P | Electrical power | W |
Worked example
What are the current and power consumption when 6 V is applied across a 10 Ω resistor?
I = 6/10 = 0.6 A is, and P = 6 × 0.6 = 3.6 W is. If the resistance is changed to 20 Ω, the current in the same 6 V will be 0.3 A. Furthermore, the slope of the graph, where the x-axis represents voltage, also decreases by half.
Common misconceptions
- Before referring to the slope of a graph as “resistance,” it is necessary to verify both the horizontal and vertical axes.
- The ammeter is connected in series, and the voltmeter in parallel, not in series-parallel.