Series resistor

A series resistor is an electrical resistor that is connected in series with an electrical component in order to limit the electrical voltage across the component or the electrical current through the component to permissible values. Components with negative differential resistance ( gas discharge tubes , arcs or tunnel diodes ) will be destroyed without a series resistor. Other uses:

• Measurement range extension of a voltmeter
• Current limitation with light emitting diodes
• Capacitor power supply for electronic circuits with low power consumption
• Limitation of the inrush current for motors or transformers by NTC .

Variants:

• Ohmic series resistor - Limits all direct and alternating currents with a high active power loss with the effective resistance of an ohmic resistor . The effective resistance is independent of the frequency.
• Capacitive series resistor - limits alternating currents with the alternating current resistance of a capacitor with almost no real power loss. The capacitive reactance decreases as the frequency increases.
• Inductive series resistor - limits frequency-stable alternating currents with the alternating current resistance of a coil with almost no real power loss. The inductive reactance increases as the frequency increases.

Example with a frequency-independent series resistor

Example of a series resistor

An ohmic series resistor is usually only used as a means of limiting the current for simple circuits and low power, since undesired heat loss occurs.

The resistance value and the power loss ( Joule heat ) of the series resistor result from the input voltage as well as the current strength and the required voltage of the component to be protected . The power loss must be less than the maximum thermal load capacity of the series resistor. If, for example, a light-emitting diode R is to be operated with a forward voltage U _R of 2.2 V on a supply voltage U of 12 V, a voltage U _V of 9.8 V must drop across the series resistor R _V. If the current through the light emitting diode is to be 15 mA, Ohm's law results in a resistance value of 653 Ω for R _V. The power loss at R _V is the product of current strength and voltage and is 147 mW. The series resistor 82% fall of the supply voltage from, and 82% of the power goes to R _V lost.

Limiting the inrush current of a switched-mode power supply to 46 A would require a series resistor of 5 Ω in the power supply line at 230 V. This would generate a power loss of 20 W at an operating current of 2 A.

Older trams (built before approx. 1965) with DC motors were controlled via series resistors. The heat loss was so great that resistance sets under the seats could take over the function of vehicle heating in winter. Here DC choppers based on thyristors have replaced the ohmic series resistors.

Example with a frequency-dependent series resistor

If high-performance components such as fluorescent lamps are operated with alternating voltage , a good level of efficiency can be achieved through an upstream reactance that limits the current without developing heat. Suitable components are capacitor and choke . The calculation of the total AC resistance for sinusoidal values ​​is done using the following formula:

${\displaystyle Z={\sqrt {R^{2}+X^{2}}}={\frac {u_{\mathrm {max} }}{i_{\mathrm {max} }}}={\frac {u_{\mathrm {eff} }}{i_{\mathrm {eff} }}}}$

and can be explained using the following example: A 60 W fluorescent lamp requires around 1 A at 60 V; this corresponds to  ≈ 60 Ω. So that 1 A is drawn from the 230 V socket,  = 230 Ω must be. By rearranging the above equation, one obtains ${\displaystyle R}$ ${\displaystyle Z}$

${\displaystyle X={\sqrt {Z^{2}-R^{2}}}={\sqrt {(230\,\Omega )^{2}-(60\,\Omega )^{2}}}=222\,\Omega }$

Using the equation for a throttle

${\displaystyle X_{L}=2\pi f\cdot L}$

and = 50 Hz you get  = 0.71 H. If you were to use a capacitor instead of the choke, this would have to have the value 14 µF. ${\displaystyle f}$ ${\displaystyle L}$

Alternatives

With larger currents and powers , power losses are particularly problematic because they cause energy costs and heat dissipation is necessary. Therefore there are the following alternatives to series resistors:

Voltage adjustment

• DC-DC converters (efficiency up to approx. 95%) generate a lower or higher direct voltage.
• Transformers generate a higher or lower AC voltage.

Current stabilization

• Special DC-DC converters can also regulate the output current, for example for the efficient operation of light-emitting diode lights.

Inrush current limitation

• To limit the inrush current, there are temperature-dependent series resistors (inrush current limiters) that reduce their resistance due to their self-heating, see NTC thermistors .
• For current limitation, also for speed control of motors, see starting resistor .

Short circuit protection

• To limit the current in the event of a short circuit or overload, a self-resetting fuse element (PTC for short, see PTC thermistor ) can be used instead of a fuse . A PTC thermistor as a series resistor for overload protection has a low electrical resistance at room temperature and rated current, which increases steeply in the event of overcurrent due to self-heating.

literature

• Klaus Tkotz: Electrical engineering. 28th edition, Verlag - Europa - Lehrmittel, Wuppertal, 2012, ISBN 978-3808531891