Contents

Section Summary

Electric current $I I size 12{I } {}$ is the rate at which charge flows, given by
$I = \frac{Δ Q}{Δ t}, I = \frac{Δ Q}{Δ t},$
where $Δ Q Δ Q$ is the amount of charge passing through an area in time $Δ t Δ t$ .
The direction of conventional current is taken as the direction in which positive charge moves.
The SI unit for current is the ampere (A), where $1 A = 1 C/s. 1 A = 1 C/s. size 12{1" A "=" 1 C/s."} {}$
Current is the flow of free charges, such as electrons and ions.
Drift velocity $v_{d} v_{d} size 12{v rSub { size 8{d} } } {}$ is the average speed at which these charges move.
Current $I I size 12{I } {}$ is proportional to drift velocity $v_{d} v_{d} size 12{v rSub { size 8{d} } } {}$ , as expressed in the relationship $I = {nqAv}_{d} I = {nqAv}_{d} size 12{I = ital "nqAv" rSub { size 8{d} } } {}$ . Here, $I I size 12{I } {}$ is the current through a wire of cross-sectional area $A A size 12{A} {}$ . The wire’s material has a free-charge density $n n size 12{n} {}$ , and each carrier has charge $q q size 12{q} {}$ and a drift velocity $v_{d} v_{d} size 12{v rSub { size 8{d} } } {}$ .
Electrical signals travel at speeds about $10^{12} 10^{12} size 12{"10" rSup { size 8{"12"} } } {}$ times greater than the drift velocity of free electrons.

A simple circuit is one in which there is a single voltage source and a single resistance.
One statement of Ohm’s law gives the relationship between current $I I$ , voltage $V V$ , and resistance $R R$ in a simple circuit to be $I = \frac{V}{R} . I = \frac{V}{R} . size 12{I = { {V} over {R} } } {}$
Resistance has units of ohms ( $Ω Ω$ ), related to volts and amperes by $1 Ω = 1 V/A 1 Ω = 1 V/A size 12{1 %OMEGA =" 1 V/A"} {}$ .
There is a voltage or $IR IR size 12{ ital "IR"} {}$ drop across a resistor, caused by the current flowing through it, given by $V = IR V = IR size 12{V = ital "IR" } {}$ .

The resistance $R R size 12{R} {}$ of a cylinder of length $L L size 12{L} {}$ and cross-sectional area $A A size 12{A} {}$ is $R = \frac{ρL}{A} R = \frac{ρL}{A} size 12{R = { {ρL} over {A} } } {}$ , where $ρ ρ size 12{ρ} {}$ is the resistivity of the material.
Values of $ρ ρ size 12{ρ} {}$ in Table 20.1 show that materials fall into three groups—conductors, semiconductors, and insulators.
Temperature affects resistivity; for relatively small temperature changes $Δ T Δ T size 12{DT} {}$ , resistivity is $ρ = ρ_{0} (1 + α Δ T) ρ = ρ_{0} (1 + α Δ T) size 12{ρ = ρ rSub { size 8{0} } $ "1 "+ αΔT $ } {}$ , where $ρ_{0} ρ_{0} size 12{ρ rSub { size 8{0} } } {}$ is the original resistivity and $α α$ is the temperature coefficient of resistivity.
Table 20.2 gives values for $α α size 12{α} {}$ , the temperature coefficient of resistivity.
The resistance $R R size 12{R} {}$ of an object also varies with temperature: $R = R_{0} (1 + α Δ T) R = R_{0} (1 + α Δ T) size 12{R = R rSub { size 8{0} } $ "1 "+ ΔαT $ } {}$ , where $R_{0} R_{0} size 12{R rSub { size 8{0} } } {}$ is the original resistance, and $R R$ is the resistance after the temperature change.

Electric power $P P size 12{P} {}$ is the rate (in watts) that energy is supplied by a source or dissipated by a device.
Three expressions for electrical power are
$P = IV, P = IV, size 12{P = ital "IV,"} {}$
$P = \frac{V^{2}}{R}, P = \frac{V^{2}}{R}, size 12{P = { {V rSup { size 8{2} } } over {R} } ","} {}$

and

$P = I^{2} R . P = I^{2} R . size 12{P = I rSup { size 8{2} } R"."} {}$
The energy used by a device with a power $P P size 12{P} {}$ over a time $t t size 12{t} {}$ is $E = Pt E = Pt size 12{E = ital "Pt"} {}$ .

Direct current (DC) is the flow of electric current in only one direction. It refers to systems where the source voltage is constant.
The voltage source of an alternating current (AC) system puts out $V = V_{0} sin 2 π ft V = V_{0} size 12{V = V rSub { size 8{0} } "sin2"π ital "ft"} {}$ , where $V V size 12{V} {}$ is the voltage at time $t t size 12{t} {}$ , $V_{0} V_{0} size 12{V rSub { size 8{0} } } {}$ is the peak voltage, and $f f size 12{f} {}$ is the frequency in hertz.
In a simple circuit, $I = V/R I = V/R size 12{I = ital "V/R"} {}$ and AC current is $I = I_{0} sin 2 π ft I = I_{0} size 12{I = I rSub { size 8{0} } "sin2"π ital "ft"} {}$ , where $I I size 12{I} {}$ is the current at time $t t size 12{t} {}$ , and $I_{0} = V_{0} /R I_{0} = V_{0} /R size 12{I rSub { size 8{0} } = V rSub { size 8{0} } ital "/R"} {}$ is the peak current.
The average AC power is $P_{ave} = \frac{1}{2} I_{0} V_{0} P_{ave} = \frac{1}{2} I_{0} V_{0} size 12{P rSub { size 8{"ave"} } = { {1} over {2} } I rSub { size 8{0} } V rSub { size 8{0} } } {}$ .
Average (rms) current $I_{rms} I_{rms} size 12{I rSub { size 8{"rms"} } } {}$ and average (rms) voltage $V_{rms} V_{rms} size 12{V rSub { size 8{"rms"} } } {}$ are $I_{rms} = \frac{I_{0}}{\sqrt{2}} I_{rms} = \frac{I_{0}}{\sqrt{2}} size 12{I rSub { size 8{"rms"} } = { {I rSub { size 8{0} } } over { sqrt {2} } } } {}$ and $V_{rms} = \frac{V_{0}}{\sqrt{2}} V_{rms} = \frac{V_{0}}{\sqrt{2}} size 12{V rSub { size 8{"rms"} } = { {V rSub { size 8{0} } } over { sqrt {2} } } } {}$ , where rms stands for root mean square.
Thus, $P_{ave} = I_{rms} V_{rms} P_{ave} = I_{rms} V_{rms} size 12{P rSub { size 8{"ave"} } = I rSub { size 8{"rms"} } V rSub { size 8{"rms"} } } {}$ .
Ohm’s law for AC is $I_{rms} = \frac{V_{rms}}{R} I_{rms} = \frac{V_{rms}}{R} size 12{I rSub { size 8{"rms"} } = { {V rSub { size 8{"rms"} } } over {R} } } {}$ .
Expressions for the average power of an AC circuit are $P_{ave} = I_{rms} V_{rms} P_{ave} = I_{rms} V_{rms}$ , $P_{ave} = \frac{V_{rms}^{2}}{R} P_{ave} = \frac{V_{rms}^{}}{R}$ , and $P_{ave} = I_{rms}^{2} R P_{ave} = I_{rms}^{} R$ , analogous to the expressions for DC circuits.

The two types of electric hazards are thermal (excessive power) and shock (current through a person).
Shock severity is determined by current, path, duration, and AC frequency.
Table 20.3 lists shock hazards as a function of current.
Figure 20.25 graphs the threshold current for two hazards as a function of frequency.

Electric potentials in neurons and other cells are created by ionic concentration differences across semipermeable membranes.
Stimuli change the permeability and create action potentials that propagate along neurons.
Myelin sheaths speed this process and reduce the needed energy input.
This process in the heart can be measured with an electrocardiogram (ECG).