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  • Explain the origin of Ohm’s law.
  • Calculate voltages, currents, or resistances with Ohm’s law.
  • Explain what an ohmic material is.
  • Describe a simple circuit.

What drives current? We can think of various devices—such as batteries, generators, wall outlets, and so on—which are necessary to maintain a current. All such devices create a potential difference and are loosely referred to as voltage sources. When a voltage source is connected to a conductor, it applies a potential difference V size 12{V} {} that creates an electric field. The electric field in turn exerts force on charges, causing current.

Ohm’s law

The current that flows through most substances is directly proportional to the voltage V size 12{V} {} applied to it. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied :

I V . size 12{I prop V.} {}

This important relationship is known as Ohm’s law    . It can be viewed as a cause-and-effect relationship, with voltage the cause and current the effect. This is an empirical law like that for friction—an experimentally observed phenomenon. Such a linear relationship doesn’t always occur.

Resistance and simple circuits

If voltage drives current, what impedes it? The electric property that impedes current (crudely similar to friction and air resistance) is called resistance     R size 12{R} {} . Collisions of moving charges with atoms and molecules in a substance transfer energy to the substance and limit current. Resistance is defined as inversely proportional to current, or

I 1 R . size 12{I prop { {1} over {R} } "."} {}

Thus, for example, current is cut in half if resistance doubles. Combining the relationships of current to voltage and current to resistance gives

I = V R . size 12{I = { {V} over {R} } "."} {}

This relationship is also called Ohm’s law. Ohm’s law in this form really defines resistance for certain materials. Ohm’s law (like Hooke’s law) is not universally valid. The many substances for which Ohm’s law holds are called ohmic    . These include good conductors like copper and aluminum, and some poor conductors under certain circumstances. Ohmic materials have a resistance R size 12{R} {} that is independent of voltage V size 12{V} {} and current I size 12{I} {} . An object that has simple resistance is called a resistor , even if its resistance is small. The unit for resistance is an ohm    and is given the symbol Ω size 12{ %OMEGA } {} (upper case Greek omega). Rearranging I = V/R size 12{I = ital "V/R"} {} gives R = V/I size 12{R= ital "V/I"} {} , and so the units of resistance are 1 ohm = 1 volt per ampere:

1 Ω = 1 V A . size 12{"1 " %OMEGA =" 1 " { {V} over {A} } "."} {}

[link] shows the schematic for a simple circuit. A simple circuit    has a single voltage source and a single resistor. The wires connecting the voltage source to the resistor can be assumed to have negligible resistance, or their resistance can be included in R size 12{R} {} .

The figure describes a simple electric circuit with a battery connected to a resistance R. The direction of current is shown to emerge from the positive terminal of a battery of voltage V, pass through the resistor, and enter the negative terminal of the battery. The current I in the circuit is V divided by R, moving in a clockwise direction.
A simple electric circuit in which a closed path for current to flow is supplied by conductors (usually metal wires) connecting a load to the terminals of a battery, represented by the red parallel lines. The zigzag symbol represents the single resistor and includes any resistance in the connections to the voltage source.

Calculating resistance: an automobile headlight

What is the resistance of an automobile headlight through which 2.50 A flows when 12.0 V is applied to it?


We can rearrange Ohm’s law as stated by I = V/R size 12{I = ital "V/R"} {} and use it to find the resistance.


Rearranging I = V/R size 12{I = ital "V/R"} {} and substituting known values gives

R = V I = 12 . 0 V 2 . 50 A = 4 . 80 Ω . size 12{R = { {V} over {I} } = { {"12" "." "0 V"} over {2 "." "50 A"} } =" 4" "." "80 " %OMEGA "."} {}


This is a relatively small resistance, but it is larger than the cold resistance of the headlight. As we shall see in Resistance and Resistivity , resistance usually increases with temperature, and so the bulb has a lower resistance when it is first switched on and will draw considerably more current during its brief warm-up period.

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