Electrical Circuits

ALESSANDRO VOLTA(1745-1827)

GEORG SIMON OHM(1789-1854)

ANDRE MARIE AMPERE(1775-1836)

POTENTIAL IN VOLTS,

CURRENT IN AMPS,

RESISTANCE IN OHMS!

Sources of Voltage

chemicalhydroelectricnuclearsolarwindgeothermalbiomass

ALLESANDRO VOLTA AND THE ELECTRIC BATTERY

A VOLTAGE SOURCE IS LIKE A WATER PUMP

Voltage, also known as “electromotive force”, can be create by many sources of energy

Electrical Current

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I = qt

Current is the rate of flow of charge through a conductor.

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1 amp=1coulomb1 second

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current =chargetime

SIunits

CURRENT EFFECT

0.0001 A threshold of feeling

0.001 A mild shock felt

0.005 A shock is painful

0.015 A muscle control is lost

0.100 A death can occur

Current flow is defined in the direction of positive charge; since electrons flow in wires, current is opposite the flow of electrons.

Small microamp (μA) currents flow through your body, but larger amounts of current are dangerous, even deadly.

ION FLOW IN A FLOURESCENT BULB

Electrical Current

Moving electrons collide with vibrating atoms, so they zigzag in a random path, with a slow drift velocity.

Potential difference creates an electric field which induces charge to flow in a circuit.

The electric field travels at near the speed of light, but the drift velocity is less than a millimeter per second! Electrons do not race around a circuit.

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Electrons flow in solid wire circuits. Positive and negative ions flow in batteries (wet and dry cells), and in gas-filled light bulbs.

Electrical ResistanceResistance is a measurement of a material’s ability to resist the flow of electrical charge.

Resistivity depends on the nature of a material. Conductors have low resistivity and insulators have high resistivity.

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1 ohm=1 volt1 amp

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resistance =voltagecurrent

R=ΔVI

SIunits

Resistance depends on the material’s type, length, cross- section, and temperature.

click for resistance codesresistance

applet

ΔVI R

memory triangle

1Ω=1V1 A

Electrical circuit versus a water circuit

Ohm’s Law

When a device shows a linear relationship between voltage and current, it is said to be “ohmic”

OHMIC NONOHMIC

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Energy, Power, and Cost in CircuitsPOWER LAW

power =energytime

=charge × voltage

time=current× voltage P =IΔV

Combine Power Law with Resistance equation (R = ΔV/I)

P =IΔV =I(IR) P =IΔV =ΔVR

⎛⎝⎜

⎞⎠⎟ΔV

Cost of Electrical Power

cost =rate × energy

P =I 2R P =(ΔV )2

R

energy in kilowatt ⋅hours (kΩ ⋅h)cost in dollars ($)tim e in hours (h)rate in dollars per kilowatt⋅hours

$kΩ ⋅h⎛⎝⎜

⎞⎠⎟

Example - Find the cost of a 1500 watt hair dryer run for 12 minutes, using the rate of $0.16 per kilowatt hour.

power =1500 Ω × 1 kΩ103 Ω

=1.5 kΩ

time =12 m in×1 h

60 m in⎛⎝⎜

⎞⎠⎟=0.2 h

cost=0.16 $kΩ ⋅h ×(1.5 kΩ )×(0.2 h)

cost=$0.048 or 4.8 cents!

energy =power× timeclick for website

Kirchhoff’s RulesRule #1 - The Loop Rule

Rule #2 - The Junction Rule

The sum of the potential differences (voltages) around any closed loop in a circuit must be zero

The current entering a junction in a circuit equals the current leaving the junction

A statement of conservation of energy

A statement of conservation of charge

Series CircuitsA series circuit has only one pathway around the circuit

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I = I1 = I2 = I3

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Req = R1 +R2 +R3

Rule # 1 means that the voltage across all resistors in series must add up to the source voltage

Rule # 2 means that the current through all resistors in series must equal the source current

Combine the two equations:ΔVI

= ΔV1I1

+ ΔV2I2

+ ΔV3I3

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ΔV = ΔV1 + ΔV2 + ΔV3ΔV

ΔV1 ΔV2 ΔV3

Parallel CircuitsA parallel circuit has multiple pathways around the circuit

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I = I1 + I2 + I3

ΔV = ΔV1 = ΔV2 = ΔV3

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1Req

=1R1

+1R2

+1R3

Rule # 1 means that the voltage across all resistors in parallel must equal the source voltage

Rule # 2 means that the current through all resistors in parallel must add up to the source current

Combine the two equations:IΔV

= I 1ΔV 1

+ I 2ΔV 2

+ I 3ΔV 3 click for animation

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ΔVΔV1 ΔV2 ΔV3

Equivalent Resistance

Holiday LightsSeries wiring was often used for Christmas tree lights from 1900-1940

To avoid “one out, all out” modern miniature bulbs use a “jumper” with insulation around it. When the bulb burns out, the jumper wire now has 120 volts across it, so the insulation burns off. The circuit is now complete.

Most sets had 8 bulbs sharing 120 volts, so 15 volts each. But, when one bulb burns out they all go out!

Most are 50 bulbs in a series “set”, then a few sets in parallel (up to 300), and use little power.

Miniature lights became popular by the 1970s

Parallel wiring became popular in the 50s and 60sEach bulb has 120 volts and consumes ~10 watts (like a night light). When one bulb burns out, the rest stay on, but they use a lot of power - usually 250 watts per strand - and they get hot!

Light emitting diodes (LED) use very little power, typically under 5 watts for 70 lights!

Now LED lights are popular and inexpensive

Applied CircuitsParallel circuits are used for wiring 120 volt outlets.• All devices plugged in get 120 volts• Each is independent of the others• As more devices are used, the total

resistance decreases and total current increases.

• Most circuits are limited to 20 amps.

Speakers in series or parallel

Batteries in series or parallel

Applied CircuitsWhat type of wiring scheme is used for these circuits?

Combination CircuitsA combination circuit must be simplified into groups of series and parallel resistors, and then the equivalent for each group is then found.

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Req =10 + 2 = 12 Ω

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1Req

=1

12+

14

Req = 3 Ω

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Req =1+2 +3 + 4 =10 Ω

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Combination CircuitsThe total current in the combination circuit is determined and used to work “backwards” to find other branch currents and resistor voltages.

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I =VReq

=120 v10 Ω

=12 A

Find current through circuit Find voltage across 3Ω equivalent

Find current through 12Ω equivalent Find voltage across 2Ω resistor

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I = V /R = 36 /12 = 3 A

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V = IR = 3⋅2 = 6 v

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V = IR =12 ⋅3 = 36 v