Ohm's law

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The idea

You connect a resistor to a battery and measure. With twice the voltage, twice as much current flows. The ratio of voltage to current stays the same: it is the resistance. This relation is Ohm's law.

What to remember

Ohm's law: For an ohmic resistor the voltage divided by the current is always the same: $R = \frac{U}{I}$ . The resistance does not change when you change the voltage.

R = \frac{U}{I}

U = R \cdot I

I = \frac{U}{R}

The unit: 1 Ω = 1 V : 1 A. Convert the current to amperes first, not milliamperes.

Characteristic curve: A characteristic curve shows how the current depends on the voltage. For an ohmic resistor it is a straight line through the origin.

A coordinate system with the voltage U to the right and the current I upward. A straight line rises from the origin. Two points are marked: at U equal to 1, I is 1, and at U equal to 2, I is 2. — The characteristic curve of an ohmic resistor is a straight line through the origin: twice the voltage gives twice the current. The digits 1 and 2 stand for equal steps on both axes.
Source: https://github.com/lernapps/elektrizitaet. Licence: CC0-1.0.

Not every part is ohmic

A bulb gets hot when it shines, and its resistance grows. Its characteristic curve is therefore bent, not a straight line. $R = \frac{U}{I}$ still holds for it at every single moment, but the value changes.

Example

A resistor on the battery

A resistor of 20 Ω is connected to 6 V. We want the current: $I = \frac{U}{R} = \frac{6 V}{20 Ω} = 0.3 A$ . The ammeter shows 0.3 A, that is 300 mA.

Practice

Task no. 1

The resistor in the circuit is unknown. Record at least three measuring points at different voltages, then calculate the resistance and enter it.

The battery can be set from 0 to 12 V in steps of 1.5 V. The voltmeter shows the voltage across the resistor, the ammeter the current. The resistor is unknown.

Solution

For example measure at 3 V, 6 V and 9 V. At 6 V the ammeter shows 0.12 A, so R = 6 V : 0.12 A = 50 Ω. The points lie on a straight line through the origin.

Exercise

Three worked tasks, each with its solution:

Task no. 1
A resistor of 20 Ω is connected to 3 V. What is the current in amperes?
Hint
$I = \frac{U}{R}$
Solution
1. $I = \frac{U}{R}$
2. $I = \frac{3 V}{20 Ω} = 0.15 A$
Right answer: 0.15 A
Task no. 2
A resistor of 100 Ω is connected to 3 V. What is the current in amperes?
Hint
$I = \frac{U}{R}$
Solution
1. $I = \frac{U}{R}$
2. $I = \frac{3 V}{100 Ω} = 0.03 A$
Right answer: 0.03 A
Task no. 3
A resistor of 20 Ω is connected to 9 V. What is the current in amperes?
Hint
$I = \frac{U}{R}$
Solution
1. $I = \frac{U}{R}$
2. $I = \frac{9 V}{20 Ω} = 0.45 A$
Right answer: 0.45 A

Exercise

Three worked tasks, each with its solution:

Task no. 1
An resistor has 9 V across it, and the ammeter shows 0.6 A. What is the resistance in Ω?
Hint
$R = \frac{U}{I}$
Solution
1. $R = \frac{U}{I}$
2. $R = \frac{9 V}{0.6 A} = 15 Ω$
Right answer: 15 Ω
Task no. 2
An resistor has 9 V across it, and the ammeter shows 0.2 A. What is the resistance in Ω?
Hint
$R = \frac{U}{I}$
Solution
1. $R = \frac{U}{I}$
2. $R = \frac{9 V}{0.2 A} = 45 Ω$
Right answer: 45 Ω
Task no. 3
An resistor has 3 V across it, and the ammeter shows 0.3 A. What is the resistance in Ω?
Hint
$R = \frac{U}{I}$
Solution
1. $R = \frac{U}{I}$
2. $R = \frac{3 V}{0.3 A} = 10 Ω$
Right answer: 10 Ω

Exercise

Solution

Right answer: The statement is true.

Because the ratio $\frac{U}{I}$ stays the same, the current grows in step with the voltage. The characteristic curve is a straight line through the origin.