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College Physics 2e

Section Summary

College Physics 2eSection Summary

20.1 Current

  • Electric current II 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 ΔtΔt.
  • 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.
  • Current is the flow of free charges, such as electrons and ions.
  • Drift velocity vdvd is the average speed at which these charges move.
  • Current II is proportional to drift velocity vdvd, as expressed in the relationship I=nqAvdI=nqAvd. Here, II is the current through a wire of cross-sectional area AA. The wire’s material has a free-charge density nn, and each carrier has charge qq and a drift velocity vdvd.
  • Electrical signals travel at speeds about 10121012 times greater than the drift velocity of free electrons.

20.2 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.
  • Resistance has units of ohms ( Ω Ω), related to volts and amperes by 1 Ω= 1 V/A1 Ω= 1 V/A.
  • There is a voltage or IRIR drop across a resistor, caused by the current flowing through it, given by V=IRV=IR.

20.3 Resistance and Resistivity

  • The resistance RR of a cylinder of length LL and cross-sectional area AA is R=ρLAR=ρLA, where ρρ is the resistivity of the material.
  • Values of ρρ in Table 20.1 show that materials fall into three groups—conductors, semiconductors, and insulators.
  • Temperature affects resistivity; for relatively small temperature changes ΔTΔT, resistivity is ρ=ρ0(1 +αΔT)ρ=ρ0(1 +αΔT), where ρ0ρ0 is the original resistivity and α α is the temperature coefficient of resistivity.
  • Table 20.2 gives values for αα, the temperature coefficient of resistivity.
  • The resistance RR of an object also varies with temperature: R=R0(1 +αΔT)R=R0(1 +αΔT), where R0R0 is the original resistance, and R R is the resistance after the temperature change.

20.4 Electric Power and Energy

  • Electric power PP is the rate (in watts) that energy is supplied by a source or dissipated by a device.
  • Three expressions for electrical power are


  • The energy used by a device with a power PP over a time tt is E=PtE=Pt.

20.5 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, where VV is the voltage at time tt, V0V0 is the peak voltage, and ff is the frequency in hertz.
  • In a simple circuit, I=V/RI=V/R and AC current is I=I0sin 2πftI=I0sin 2πft, where II is the current at time tt, and I0=V0/RI0=V0/R is the peak current.
  • The average AC power is Pave=12I0V0Pave=12I0V0.
  • Average (rms) current IrmsIrms and average (rms) voltage VrmsVrms are Irms=I02Irms=I02 and Vrms=V02Vrms=V02, where rms stands for root mean square.
  • Thus, Pave=IrmsVrmsPave=IrmsVrms.
  • Ohm’s law for AC is Irms=VrmsRIrms=VrmsR.
  • Expressions for the average power of an AC circuit are Pave= Irms VrmsPave= Irms Vrms, Pave = Vrms2RPave = Vrms2R, and Pave= Irms2RPave= Irms2R, analogous to the expressions for DC circuits.

20.6 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 20.3 lists shock hazards as a function of current.
  • Figure 20.22 graphs the threshold current for two hazards as a function of frequency.

20.7 Nerve Conduction–Electrocardiograms

  • 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).
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