# Linear resistance

An electrical resistance is called a linear resistance if an electrical voltage applied to it and the strength of the electrical current flowing through it are proportional to one another . In other words, for a linear resistance, the ratio is independent of and from . The voltage-current characteristic for a linear resistance is a straight line through the origin of the coordinates . ${\ displaystyle U}$ ${\ displaystyle I}$${\ displaystyle U / I}$${\ displaystyle U}$${\ displaystyle I}$

Characteristic curve of a linear resistance

The best-known linear resistance is an ohmic resistance , which directly stands for the aforementioned ratio ${\ displaystyle R}$

${\ displaystyle {\ frac {U} {I}} = R}$

and is by definition a constant independent of and . These quantities must be equal quantities or instantaneous values in the case of quantities that can change over time. ${\ displaystyle U}$${\ displaystyle I}$

Especially for sinusoidal alternating quantities, the inductance and the capacitance also behave as linear resistances with regard to the rms values and amplitudes of the alternating quantities. If and stand for the rms values, their ratio is also a constant, albeit one that depends on the frequency , see AC resistance and Ohm's law of AC technology${\ displaystyle L}$ ${\ displaystyle C}$${\ displaystyle U}$${\ displaystyle I}$ ${\ displaystyle f}$

${\ displaystyle {\ frac {U} {I}} = 2 \, \ mathrm {\ pi} \, f \ cdot L \ quad {\ text {and}} \ quad {\ frac {U} {I}} = {\ frac {1} {2 \ mathrm {\ pi} f \ cdot C}} \.}$

There is no proportionality between the time-dependent instantaneous values ​​of the alternating variables on and because of a phase shift , see reactive current . ${\ displaystyle L}$${\ displaystyle C}$

With a sinusoidal voltage across a linear resistor, the current is also sinusoidal and of the same frequency. In contrast, resistances other than linear always generate harmonics - a process known as non-linear distortion . The absence of harmonics is another characteristic of linear resistance.

Examples of non-linear resistances are semiconductor components and magnetic components ( chokes , transformers ) with non-linear characteristics.

## literature

• Dieter Zastrow: Electrical engineering: a basic textbook . Vieweg + Teubner, 2010, page 252.
• Wilfried Weißgerber: Electrical engineering for engineers 1 . Vieweg + Teubner, 2013, page 12 ff.
• Wilfried Weißgerber: Electrical engineering for engineers 2 . Vieweg + Teubner, 2013, page 28 ff.

## Individual evidence

1. EN 80000-6: 2013, quantities and units - Part 6: Electromagnetism. Entry 6-46