If voltage drives current, what impedes it? The electric property that impedes current (crudely similar to friction and air resistance) is called resistance RR 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∝1R.I∝1R. size 12{I prop { {1} over {R} } "."} {}

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

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

(3)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 RR size 12{R} {} that is independent of voltage VV size 12{V} {} and current II 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 ΩΩ size 12{ %OMEGA } {} (upper case Greek omega). Rearranging I=V/RI=V/R size 12{I = ital "V/R"} {} gives R=V/IR=V/I size 12{R= ital "V/I"} {}, and so the units of resistance are 1 ohm = 1 volt per ampere:

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

(4)Figure 1 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 RR size 12{R} {}.

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

*Strategy*

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

*Solution*

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

R=VI=12.0 V2.50 A= 4.80 Ω.R=VI=12.0 V2.50 A= 4.80 Ω. size 12{R = { {V} over {I} } = { {"12" "." "0 V"} over {2 "." "50 A"} } =" 4" "." "80 " %OMEGA "."} {}

(5)
*Discussion*

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.

Resistances range over many orders of magnitude. Some ceramic insulators, such as those used to support power lines, have resistances of 1012Ω1012Ω size 12{"10" rSup { size 8{"12"} } ` %OMEGA } {} or more. A dry person may have a hand-to-foot resistance of 105Ω105Ω size 12{"10" rSup { size 8{5} } ` %OMEGA } {}, whereas the resistance of the human heart is about 103Ω103Ω size 12{"10" rSup { size 8{3} } ` %OMEGA } {}. A meter-long piece of large-diameter copper wire may have a resistance of 10−5Ω10−5Ω size 12{"10" rSup { size 8{ - 5} } ` %OMEGA } {}, and superconductors have no resistance at all (they are non-ohmic). Resistance is related to the shape of an object and the material of which it is composed, as will be seen in Resistance and Resistivity.

Additional insight is gained by solving I=V/RI=V/R size 12{I = ital "V/R"} {} for V,V, size 12{V} {} yielding

V=IR.V=IR. size 12{V = ital "IR."} {}

(6)This expression for VV size 12{V} {} can be interpreted as the *voltage drop across a resistor produced by the flow of current *II size 12{I} {}. The phrase IRIR size 12{ ital "IR"} {} *drop* is often used for this voltage. For instance, the headlight in Example 1 has an IRIR size 12{ ital "IR"} {} drop of 12.0 V. If voltage is measured at various points in a circuit, it will be seen to increase at the voltage source and decrease at the resistor. Voltage is similar to fluid pressure. The voltage source is like a pump, creating a pressure difference, causing current—the flow of charge. The resistor is like a pipe that reduces pressure and limits flow because of its resistance. Conservation of energy has important consequences here. The voltage source supplies energy (causing an electric field and a current), and the resistor converts it to another form (such as thermal energy). In a simple circuit (one with a single simple resistor), the voltage supplied by the source equals the voltage drop across the resistor, since PE=qΔVPE=qΔV size 12{"PE"=qΔV} {}, and the same qq size 12{q} {} flows through each. Thus the energy supplied by the voltage source and the energy converted by the resistor are equal. (See Figure 2.)

In a simple electrical circuit, the sole resistor converts energy supplied by the source into another form. Conservation of energy is evidenced here by the fact that all of the energy supplied by the source is converted to another form by the resistor alone. We will find that conservation of energy has other important applications in circuits and is a powerful tool in circuit analysis.

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