Section Summary

Sections
Section Summary

Section Summary

3.1 Current

  • 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.

3.2 Ohm’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 R R in a simple circuit to be I=VR.I=VR. 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 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" } {}

3.3 Resistance 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 α α 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 R R is the resistance after the temperature change.

3.4 Electric 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"} {}

3.5 Alternating 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= Irms Vrms,Pave= Irms Vrms, Pave = Vrms2RPave = Vrms2R, and Pave= Irms2R,Pave= Irms2R, analogous to the expressions for DC circuits.

3.6 Electric 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.