Electrical Engineering BMT & UFC › Ideal Components

Resistor as a Component

Description

The formulas from the physical fundamentals apply to the resistor as a component:

\[ \begin{gathered} R = \rho \cdot \frac{l}{A} = \frac{l}{\kappa \cdot A} \\[4pt] \text{With } \rho\text{: material parameter, resistivity} \\ \kappa\text{: material parameter, conductivity} \\ l\text{: length} \\ A\text{: area} \\[4pt] U = R \cdot I \end{gathered} \]

The ohmic resistor is a linear component, because current and voltage are related linearly by a straight-line equation.

Characteristic of a resistor R = 3 Ω: voltage U over current I

The slope of the straight line in the graph of U over I is the resistance value R.

Modelling

In the circuit diagram, a resistor is modelled as a rectangle with two terminals.

Power and energy

A resistor converts electrical energy into thermal energy. A resistor gets warm when current flows. It is thus the first representative of the components that convert energy into another form. For a resistor, the following applies:

\[ \begin{gathered} P = U \cdot I \\[4pt] U = R \cdot I \\[4pt] P = \frac{U^2}{R} = R \cdot I^2 \end{gathered} \]

At constant power (i.e. with constant values of U and I), the thermal energy in the resistor increases linearly. So the resistor gets warmer and warmer from a starting value. The starting value is the temperature of the resistor before the current flows.

Use in a circuit

The resistor is rarely used to generate heat. It is used for this, for example, in a hotplate. Usually, resistors of a certain size ensure that voltage and current at other loads in a circuit have the right values for operating these loads. More on this in the chapter on circuit analysis.

Further information (in German)

Ohm's law

Resistance formula

Building circuits