Sections
Section Summary

# Section Summary

### 3.1Current

• Electric current $II size 12{I } {}$ is the rate at which charge flows, given by
$I=ΔQΔt,I=ΔQΔt,$
where $ΔQΔQ$ is the amount of charge passing through an area in time $Δt.Δt.$
• 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 $vdvd size 12{v rSub { size 8{d} } } {}$ is the average speed at which these charges move.
• Current $II size 12{I } {}$ is proportional to drift velocity $vd,vd, size 12{v rSub { size 8{d} } } {}$ as expressed in the relationship $I=nqAvd.I=nqAvd. size 12{I = ital "nqAv" rSub { size 8{d} } } {}$ Here, $II size 12{I } {}$ is the current through a wire of cross-sectional area $A.A. size 12{A} {}$ The wire's material has a free-charge density $nn size 12{n} {}$, and each carrier has charge $qq size 12{q} {}$ and a drift velocity $vd.vd. size 12{v rSub { size 8{d} } } {}$
• Electrical signals travel at speeds about $10121012 size 12{"10" rSup { size 8{"12"} } } {}$ times greater than the drift velocity of free electrons.

### 3.2Ohm’s Law: Resistance and Simple Circuits

• 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 $RR$ in a simple circuit to be $I=VR.I=VR. size 12{I = { {V} over {R} } } {}$
• Resistance has units of ohms ($ΩΩ$), 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 $IRIR size 12{ ital "IR"} {}$ drop across a resistor, caused by the current flowing through it, given by $V=IR.V=IR. size 12{V = ital "IR" } {}$

### 3.3Resistance and Resistivity

• The resistance $RR size 12{R} {}$ of a cylinder of length $LL size 12{L} {}$ and cross-sectional area $AA size 12{A} {}$ is $R=ρLA,R=ρLA, size 12{R = { {ρL} over {A} } } {}$ where $ρρ size 12{ρ} {}$ is the resistivity of the material.
• Values of $ρρ size 12{ρ} {}$ in Table 3.1 show that materials fall into three groups—conductors, semiconductors, and insulators.
• Temperature affects resistivity; for relatively small temperature changes $ΔT,ΔT, size 12{DT} {}$ resistivity is $ρ=ρ0(1 +αΔT)ρ=ρ0(1 +αΔT) size 12{ρ = ρ rSub { size 8{0} } $$"1 "+ αΔT$$ } {}$, where $ρ0ρ0 size 12{ρ rSub { size 8{0} } } {}$ is the original resistivity and $αα$ is the temperature coefficient of resistivity.
• Table 3.2 gives values for $αα size 12{α} {}$, the temperature coefficient of resistivity.
• The resistance $RR size 12{R} {}$ of an object also varies with temperature: $R=R0(1 +αΔT),R=R0(1 +αΔT), size 12{R = R rSub { size 8{0} } $$"1 "+ ΔαT$$ } {}$ where $R0R0 size 12{R rSub { size 8{0} } } {}$ is the original resistance, and $RR$ is the resistance after the temperature change.

### 3.4Electric Power and Energy

• Electric power $PP size 12{P} {}$ is the rate (in watts) that energy is supplied by a source or dissipated by a device.
• Three expressions for electrical power are
$P=IV,P=IV, size 12{P = ital "IV,"} {}$
$P=V2R,P=V2R, size 12{P = { {V rSup { size 8{2} } } over {R} } ","} {}$

and

$P=I2R.P=I2R. size 12{P = I rSup { size 8{2} } R"."} {}$
• The energy used by a device with a power $PP size 12{P} {}$ over a time $tt size 12{t} {}$ is $E=Pt.E=Pt. size 12{E = ital "Pt"} {}$

### 3.5Alternating Current versus Direct Current

• 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 $V=V0sin 2πftV=V0sin 2πft size 12{V = V rSub { size 8{0} } "sin2"π ital "ft"} {}$, where $VV size 12{V} {}$ is the voltage at time $t,t, size 12{t} {}$$V0V0 size 12{V rSub { size 8{0} } } {}$ is the peak voltage, and $ff size 12{f} {}$ is the frequency in hertz.
• In a simple circuit, $I=V/RI=V/R size 12{I = ital "V/R"} {}$ and AC current is $I=I0sin 2πftI=I0sin 2πft size 12{I = I rSub { size 8{0} } "sin2"π ital "ft"} {}$, where $II size 12{I} {}$ is the current at time $tt size 12{t} {}$, and $I0=V0/RI0=V0/R size 12{I rSub { size 8{0} } = V rSub { size 8{0} } ital "/R"} {}$ is the peak current.
• The average AC power is $Pave=12I0V0.Pave=12I0V0. size 12{P rSub { size 8{"ave"} } = { {1} over {2} } I rSub { size 8{0} } V rSub { size 8{0} } } {}$
• Average (rms) current $IrmsIrms size 12{I rSub { size 8{"rms"} } } {}$ and average (rms) voltage $VrmsVrms size 12{V rSub { size 8{"rms"} } } {}$ are $Irms=I02Irms=I02 size 12{I rSub { size 8{"rms"} } = { {I rSub { size 8{0} } } over { sqrt {2} } } } {}$ and $Vrms=V02Vrms=V02 size 12{V rSub { size 8{"rms"} } = { {V rSub { size 8{0} } } over { sqrt {2} } } } {}$, where rms stands for root mean square.
• Thus, $Pave=IrmsVrms.Pave=IrmsVrms. size 12{P rSub { size 8{"ave"} } = I rSub { size 8{"rms"} } V rSub { size 8{"rms"} } } {}$
• Ohm's law for AC is $Irms=VrmsRIrms=VrmsR size 12{I rSub { size 8{"rms"} } = { {V rSub { size 8{"rms"} } } over {R} } } {}$.
• Expressions for the average power of an AC circuit are $Pave=IrmsVrms,Pave=IrmsVrms,$$Pave=Vrms2RPave=Vrms2R$, and $Pave=Irms2R,Pave=Irms2R,$ analogous to the expressions for DC circuits.

### 3.6Electric Hazards and the Human Body

• 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 3.3 lists shock hazards as a function of current.
• Figure 3.28 graphs the threshold current for two hazards as a function of frequency.