Ohm's law is one of the most important relationships in electrical engineering. It describes how voltage, current and electrical resistance are linked in a circuit. You only need to know two of these quantities to work out the third. In this article we explain the formula, the SI units, and we walk through the calculations step by step using a concrete example.
What does Ohm's law state?
Ohm's law states that the current flowing through a conductor is directly proportional to the voltage applied across its ends and inversely proportional to the resistance. We write the basic formula as:
- U = I × R — voltage equals current times resistance
- I = U / R — current equals voltage divided by resistance
- R = U / I — resistance equals voltage divided by current
The symbol U stands for voltage, I for current, and R for electrical resistance.
Units in the SI system
Each quantity has its own base unit:
- Voltage U — volt (V)
- Current I — ampere (A)
- Resistance R — ohm (Ω)
- Power P — watt (W)
Remember the prefixes: 1 kΩ is 1000 Ω, and 1 mA is 0.001 A. Before substituting into the formula, always reduce the values to the base units.
Step-by-step worked example
We have a light bulb supplied with a voltage of U = 12 V, through which a current of I = 0.5 A flows. We want to calculate the resistance and the power.
- We choose the formula for resistance: R = U / I.
- We substitute the values: R = 12 V / 0.5 A.
- We calculate: R = 24 Ω.
- We find the power from the formula P = U × I = 12 V × 0.5 A = 6 W.
So the bulb has a resistance of 24 ohms and draws 6 watts of power. Knowing these figures, you can select a suitable fuse or wire.
Electrical power and Ohm's law
Power in a circuit is directly linked to Ohm's law. The basic formula is P = U × I. Combining it with Ohm's law gives two derived forms:
- P = I² × R — when we know the current and resistance
- P = U² / R — when we know the voltage and resistance
For our bulb: P = I² × R = 0.5² × 24 = 0.25 × 24 = 6 W. The result matches the previous calculation, which confirms the figures are correct.
Second example: calculating the current
We connect a heater with a resistance of R = 46 Ω to a socket with a voltage of U = 230 V. We want to know how much current flows through it.
- We choose the formula for current: I = U / R.
- We substitute the values: I = 230 V / 46 Ω.
- We calculate: I = 5 A.
- Power of the heater: P = U × I = 230 × 5 = 1150 W.
The heater draws a current of 5 amperes and has a power of 1150 watts. Such a current will not overload a typical 16 A fuse, so the installation is safe.
Connecting resistors in series and in parallel
Circuits often contain several resistors. The way they are connected affects the equivalent resistance:
- Series connection: resistances add up, R = R₁ + R₂ + R₃. The same current flows through every resistor.
- Parallel connection: we add the reciprocals of the resistances, 1/R = 1/R₁ + 1/R₂. The same voltage appears across each resistor.
For two 6 Ω resistors connected in series the equivalent resistance is 12 Ω, while connected in parallel it is only 3 Ω.
When does Ohm's law not apply?
Ohm's law applies to ohmic elements, that is, those whose resistance stays constant regardless of voltage. It does not apply directly to diodes, transistors or bulbs with a tungsten filament, where the resistance changes with temperature. In school problems we usually assume an ideal resistor with a constant value R, which greatly simplifies the calculations.
Most common mistakes
- Mixing up units — entering milliamperes instead of amperes understates the current a thousandfold.
- Wrong rearrangement of the formula — remember that R = U / I, not U × I.
- Ignoring power — in many problems the power, not just the resistance, is the key quantity.
- Ignoring how resistors are connected — the equivalent resistance depends on whether the connection is in series or in parallel.
Frequently asked questions
- How can I remember the Ohm's law formulas? A triangle helps: U at the top, with I and R below. Covering the quantity you are looking for reveals the formula.
- Does Ohm's law work for alternating current? Yes, for ohmic elements. For coils and capacitors we use impedance instead of resistance.
- What does a resistance of 0 Ω mean? That is a short circuit. In the formula I = U / R it would give an infinitely large current, which is why short circuits are dangerous.
Summary
Ohm's law U = I × R lets you find any of the three electrical quantities when you know the other two. You only need to remember the three rearrangements of the formula and keep an eye on the SI units. With that, you can quickly calculate the resistance of a circuit, the current or the required voltage, as well as the electrical power.
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