What are the dimensions of the electrical resistance

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The specific resistance

In the section Definition of Electrical Resistance, we have already learned that the resistance must be material-dependent. In the following we want to explain which geometric dimensions determine the resistance.

Does the length affect the resistance? For this we think of the length of a resistance wire, composed of several pieces of the same length.

With this arrangement of the wire we use the series connection: When resistors are connected in series, the total resistance results from the sum of the individual resistances. Hence applies. This means that if a resistance is lengthened by four times, it also has four times the resistance.

In general we get:, where is the length of the resistor.

Does the cross-sectional area of ​​the wire also affect the resistance? We imagine the cross-sectional area of ​​a resistance wire composed of several pieces of the same area.

With this structure of the wire we use the parallel connection: With the parallel connection of resistors, the reciprocal value of the total resistance is calculated from the sum of the reciprocal values ​​of the individual resistances. Hence applies. This means that if the cross-sectional area of ​​a resistor is increased to four times, it only has a quarter of the resistance.

One generally obtains: where is the cross-sectional area of ​​the resistor.

In summary, the resistance is proportional to its length and indirectly proportional to its cross-sectional area. The specific resistance is introduced as a constant of proportionality, abbreviated by the Greek letter, so that the above formula is called:.

The specific resistance
The formula for calculating the resistance applies: with the length and the area of ​​the resistance. It is now referred to as the specific resistance, which is characteristic of the respective material. The specific resistance is given in the unit 1 Ω⋅.

The following table lists various specific resistances at a temperature of 20 ° C.

Tab. 1
material / Ω
aluminum 0,026
iron 0,10
copper 0,017
silver 0,016
mercury 0,96
Constantan 0,50
Work order

At a barbecue party in summer you want to set up the electric grill in the garden. Since there is no socket nearby, the grill is connected to the socket with a cable drum that is 20 meters long. Estimate by how much the resistance of this circuit is increased if the cable drum has copper wires with the cross-sectional area of!

solution