Ohm's Law

If you wish to determine mathematically what is happening in electrical terms in simple or even complex circuits, you have to know that the current  I is dependent on two factors, the voltage U and the resistance R. This dependency was described in Ohm's law named after the German physicist Georg Simon Ohm. To elaborate on this, first consider the simple circuit shown below.

Resistor Circuits !

If, for example, you double the voltage in this circuit, you will find that the current also increases two fold. If, whilst keeping the voltage constant, you double the resistance, the current is reduced by half. Both observations taken together are summarised in Ohm's law:

The current I increases with increasing voltage U and decreases with increasing resistance R. The current changes in direct proportion to the voltage and in inverse proportion to the resistance.

As a mathematical expression Ohm's law is stated thus:

Resistor Circuits !

If you resolve the equation for voltage U, the following equation is obtained

Resistor Circuits !

which describes the voltage drop across a resistor through which a current I flows. If you rearrange the equation so that the resistance R appears on the left-hand side, you obtain the following relationship:

Resistor Circuits !

which permits the computation of the resistance from the current and voltage.

(Note: here we use the symbol U to represent voltage, as is conventional in some European countries. Elsewhere it is common to see voltage represented by the letter V, so that Ohm's law is written V = I · R, for example)

Note: resistances for which Ohm' law applies (i.e. proportionality between current and voltage) are also referred to as ohmic resistances. Metal conductors usually present an ohmic resistance, whereas the resistance of conductive fluids does not fulfil the criteria of Ohm's law. 

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