Section Summary

Current

• Electric current II is the rate at which charge flows, given byI=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.

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 II, voltage VV, and resistance RR in a simple circuit to be I=VR.I=VR.
• Resistance has units of ohms (ΩΩ), 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.

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 αα 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 RR is the resistance after the temperature change.

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 areP=IV,P=IV,P=V2R,P=V2R,andP=I2R.P=I2R.
• The energy used by a device with a power PP over a time tt is E=PtE=Pt.

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=I02√Irms=I02 and Vrms=V02√Vrms=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=IrmsVrmsPave=IrmsVrms, Pave=V2rmsRPave=Vrms2R, and Pave=I2rmsRPave=Irms2R, analogous to the expressions for DC circuits.

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.

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).