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
- 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!
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