College Physics for AP® Courses 2e

# Section Summary

## 20.1Current

• 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.

## 20.2Ohm’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 $R R$ 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 $V=IRV=IR$.

## 20.3Resistance 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.

## 20.4Electric 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
$P=IV,P=IV,$
$P=V2R,P=V2R,$

and

$P=I2R.P=I2R.$
• The energy used by a device with a power $PP$ over a time $tt$ is $E=PtE=Pt$.

## 20.5Alternating 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 $V=V0sin 2πftV=V0sin 2πft$, 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.

## 20.6Electric 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 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.

## 20.7Nerve 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).