Ohm’s law

Theory and practice

[204] This is the SI unit of resistance. 1 ohm is the electrical resistance between two points on a conductor when a constant potential difference of one volt between the two points causes a current of one ampere in the conductor.

Eq. Unit of resistance

Most, if not all, components have internal resistance, such as batteries. It is not a property that is easily measurable. Circuits intended to show some principles assume that, for example, the power source is an ideal cell and any internal resistances are compensated by additional components of such a circuit, assuming a certain margin of error.

Feeding a resistor with too low resistance in a single-element system causes de facto short-circuit of the contacts of the power source, e.g. a battery, which will probably lead to its degradation. The larger the cross-section of the conductor, the lower its resistance and the larger the surface capable of dissipating heat – hence the conductor can withstand a higher current intensity.

[202] The intensity of the current through a conductor is directly proportional to the voltage applied between its ends. If the resistance is kept constant, then increasing the voltage will increase the amperage. At constant voltage, increasing the resistance reduces the amperage.

[202] Assuming that the battery has a voltage of 9V as the source of electrical energy and the resistor shows a resistance of 10k Ω, then the ammeter, which is connected in series to the circuit, will give a result of about 900mA. This result should also include the internal resistance of the ammeter and the actual battery voltage. The resistance of the circuit itself should also be taken into account. The result of 0.9A will therefore only be an approximation.

Fig. An example of a circuit with a battery, resistor and ammeter (p01)

The next example will show how we measure the resistance of series-connected resistors. It is simply their sum.

Fig. Sum of series resistance values ​​(p02)

For comparison, we can connect the resistors in parallel. Here, the calculation of the output value of the resistance is slightly different and is described by the formula:

Eq. Parallel resistance
Fig. Connecting resistors in parallel (p03)

With this connection, the effective resistance will be less than the smallest component in such a parallel configuration.

[Georg Simon Ohm] He formulated (1827) a law describing the relationship between the intensity of an electric current and electric voltage, known today as Ohm’s law. He investigated the heating of conductors with the flow of electric current. He found the dependence of resistance from the geometric form of the conductor” [W]

Examples available at https://github.com/michalasobczak/simple_hpc/tree/master/SeriesPartOne

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