Electricity Basic electrical instruments and symbols;

Electric charge and electric field; EP; Capacitance; Current, Resistance, and

EMF; Circuits

Electric charge and Electric field

Field Type Caused By

gravity mass

electric charge

magnetic moving charge

Electric charge and Electric field

Charge is not created or destroyed, it is only transferred.

Conductors and Insulators

transfers charge on contact

does not transfer

charge on contact

Objects usually have equal numbers of positive and negative  ? , but it isn't too hard to temporarily create an imbalance. Have you ever received a  ? after walking across a carpet? As your feet shuffle across the carpet, they pick up extra ? . Those electrons can't wait for you to touch a ?. As soon as your hand is close, they jump off with a shock and a spark of ? . 

Charging Processes

By contactPolarizationInduction

Coulomb’s law

The magnitude of the electric force between two point charges is

directly proportional to the product of the charges and inversely proportional to the square of the

distance between them

Coulomb’s law

Fα q1q2 Fα 1/r2

F= k [q1q2/r2]k=9.0x109Nm2/C2

Example

• Two point charges, q1= +25nC and q2= -75nC, are separated by a distance of 3.0cm. Find the magnitude and direction of a) the electric force that q1 exerts on q2 b) and the electric force that q2 exerts on q1.

• 0.019N towards each other

Electric Field, Electric Forces, and Electric field lines

• Michael Faraday, in the 1830’s, came up with the idea of an Electric Field

• Electric field is the force per unit charge

Electric Field, Electric Forces, and Electric field lines

• Electric field of a point charge is:

E= F/q0

• The E at r is:E=kq1/r2

Example

• What is the magnitude of the electric field at a point 2.0m from a point charge q=4.0nC. (The point charge could represent any small charged object with this value of q, provided the dimensions of the object are much less than the distance from the object to the field point)

• 9.0N/C

Electric Field, Electric Forces, and Electric field lines

Like charges(++) Opposite charges(+-)

Electric Field, Electric Forces, and Electric field lines

E-field lines begin on +

charges and end on -

charges(or infinity).

They enter or leave charge symmetrically.

The number of lines entering or leaving a

charge is proportional to

the charge

The density of lines indicates the strength of E at that point.

No two field lines can cross.

Electric Potential Energy

In a uniform field In a uniform field

+ + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - - -

+

+

a

b

+ + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - - -

+

+

b

a

Electric Potential Energy

In a uniform field

• Wa-b=Fd=q0Ed

• U=q0Ey• Wa-b=-ΔU=-(Ub-Ua)

• -ΔU=-q0E(yb-ya)

In a uniform field

• If ya > yb, q0 moves in the same direction as E; field does a pos. Work, U decreases

• If ya < yb, q0 moves in the opp. direction as E; field does a neg. Work, U increases

Electric Potential Energy

Two point charges

• U=[k(qq0)]/r

• U= (1/4πε0)(qq0/r)

Two point charges

a+

b

+

+

rra

rb

q0

Electric Potential

Potential energy per unit charge

V=U/q0

1V=1volt=1J/C

Electric Potential

Due to a point charge

• V= U/q0

• V=(1/4πε0)(q/r)

Collection of point charges

• V= U/q0

• V=(1/4πε0)Σ(qI/rI)

Electric Potential= Work/charge Wab/q0= -ΔU/q0=-(Ub-Ua)/q0=-(Vb-Va)= Va-Vb

Example

• How much work is required to move a charge of 4 nC from a point 2m away to a point 0.5 m away from a point charge of 60 nC? What is the potential difference between these points?

• 3.24x10-6J; Vb-a=810 V

Capacitors and Capacitance

any 2 conductors separated

by an insulator

Stores electric

potential energy

Stores charge

Capacitors and Capacitance

Doubling the magnitude of

Q

Doubles the

electric field

Doubles Potential

difference

Capacitors and Capacitance

The ratio of charge to Potential

difference

Capacitance:1F=farad=1C/V C=Q/Vab

Capacitors and Capacitance in vacuum

Simplest capacitor consists of 2 parallel plates w/area A and

dist. d

When the plates are charged, E is almost

completely localized in the region between the plates

E between the plates is uniform and distributed

over their opposing surfaces

Thus it is a parallel plate capacitor

Capacitors and Capacitance in vacuum

For parallel-plate capacitor in vacuum C= Q/Vab = ε0(A/d)

ε0Permittivity of space

constant= 8.85x10-12F/m

Capacitors and Capacitance

In Series1/Ceq= 1/C1+1/C2+1/C3..

The reciprocal of the equivalent capacitance of a series combination equals the sum of the reciprocals of the individual capacitances.

In Parallel Ceq= C1+C2+C3..

The equivalent capacitance of a parallel combination equals the sum of the individual capacitances.

Capacitors and Capacitance

In Series1/Ceq= 1/C1+1/C2+1/C3..

Q=Q1=Q2=Q3

V1= Q/C1

V2= Q/C2

V= V1+V2+V3+..

In Parallel Ceq= C1+C2+C3..

V=V1=V2=V3

Q1= VC1

Q2= VC2

Q= Q1+Q2+Q3+..

Example

• A parallel-plate capacitor has a capacitance of 1.0F. If the plates are 1.0mm apart, what is the area of the plates?

• 1.1x108m2

Example

• Let C1=6.0μF, C2= 3.0 μF, and Vab= 18V. Find the equivalent capacitance, and find the charge and potential difference for each capacitor when the two capacitors are connected a) in series; b) in parallel

Series: Ceq=2.0 μF; Q= 36 μC; Vac=6.0V, Vcb= 12VParallel: Ceq=9.0 μF; Q1= 108μC, Q2= 54 μC; V= 18V

Atoms, the basic building blocks of ?, are made of three basic components: protons, neutrons and ?. The protons and neutrons cluster together to form the  ?, which is the  ? part of the atom, and the  ? orbit about the nucleus. Protons and electrons each carry a ? . Protons carry a  ? charge while electrons carry a  ? charge. Neutrons are  ? - they carry no charge at all. 

Current, Resistance, and EMF

CurrentIs any motion of charge from one region to

another

I=dQ/dt=nqvdA

General expression for current

J=I/A=nqvd

Vector current density

Current, Resistance, and EMF

Resistivity

Ratio of the magnitudes

of E and J

ρ=E/JJ is nearly directly prop. to E: Ohm’s

law

Current, Resistance, and EMF

Resistivity and

temperatureρ(T)=ρ0[1+α(T-T0)]

ρ0 is resistivity at T0; α is the temp. coefficient of

resistivity

Current, Resistance, and EMF

ResistivityRatio of the

magnitudes of E and J

R=ρL/A (relationship between R and

ρ)

ResistanceRatio of V to I for a

particular conductor

(Ohm)R=V/I

Current, Resistance, and EMF

The influence that makes current flow

from lower to higher potential

Electromotive force or emf (E)

(1V=1J/C)

V=E=IR

Current, Resistance, and EMF

Series

• It=I1=I2=I3

• Vt=V1+V2+V3+…

• Rt=R1+R2+R3+…

Parallel• It=I1+I2+I3

• Vt=V1=V2=V3

• 1/Rt=1/R1+1/R2+1/R3

Resistors in Series and Parallel

Junction/ node/ branch

point

A point in a circuit where 3 or more conductors

meet

loopIs any closed conducting path

Resistors in Series and Parallel

• Kirchhoff’s junction rule:– The algebraic sum of the currents into any

junction is zero. (ƩI=0)• Kirchhoff’s loop rule:

– The algebraic sum of the potential differences in any loop, including those associated with emf’s and those of resistive elements, must equal zero. ( V=0)Ʃ

Example

The circuit contains 2

batteries, each with an emf and

an internal resistance, and 2

resistors. Find the current into

the circuit.I=0.5A

Electric Power

Energy consumption

Electric power

• It is the amount of electrical energy one uses up per second

• SI unit is Watt• 1hp= 746 Watts

Examples

• A horse pulled a load with a force of 200N through a distance of 100m in 20 seconds. What is the power of the horse?

Ans. 1000W• A man lifted a load of 80kg to a height of

1.5m in 3 seconds. What is the power in watts?

Ans. 392W

Energy cost

Example

• A 1.5hp air-conditioning unit is used for 10h. How much electrical energy (work) did it consume?

• 11.19kWh• 5.50/kWh• Cost= 65.45Php