Electrical Circuits

ALESSANDRO VOLTA(1745-1827)

GEORG SIMON OHM(1789-1854)

ANDRE MARIE AMPERE(1775-1836)

Sources of Voltage (Energy)

solargeothermalwind

hydroelectricchemicalpiezoelectric

nuclear

ALLESANDRO VOLTA AND THE ELECTRIC BATTERY

A VOLTAGE SOURCE IS LIKE A WATER PUMP

biomass

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

Electrical Current

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

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1 amp=1coulomb1 second

A =Cs

€

current =charge

timeSIunit

s

CURRENT EFFECT

0.0001 Athreshold of

feeling

0.001 Amild shock

felt

0.005 Ashock is painful

0.015 Amuscle control

is lost

0.100 Adeath 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 (A) currents flow through your body, but larger amounts of current are dangerous, even deadly.

Electrical Current

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

Potential difference creates an electric field in a circuit. The electric field induce charge to flow.

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

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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.

R=ΔVI

Ω=V

ASIunit

s

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

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resistance codesresistance

applet

Alternating versus Direct Current

Alternating current (ac) switches the direction of the current back and forth at 60 times per second (60 Hertz).North America uses ac for its power grid because it was safer and more reliable when infrastructure began.

Most devices use direct current so a transformer converts ac to dc often at lower voltage. Direct energy conversion devices like light bulbs, heaters, can run off ac or dc

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ALTERNATING CURRENT

DIRECT CURRENT

Batteries provide direct current (to increase battery life).

Thomas Edison brought direct current to the masses. Nikola Tesla proved alternating current to be more efficient.

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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.

slope = 1/R

voltage

ONE-WAY (DIODE)

slope = 1/R

voltage

slope = 1/R

voltage

Energy, Power, and Cost in CircuitsPOWER LAW

Combine Power Law with Resistance equation

Cost of Electrical Power Example - Find the cost of a 1500 watt

hair dryer run for 12 minutes, using the rate of $0.10 per kilowatt hour.

power =1500 W×1 kW103 W

=1.5 kW

time=12 min×1 h

60 min⎛⎝⎜

⎞⎠⎟=0.2 h

cost=0.10 $kW⋅h ×(1.5 kW)×(0.2 h)

cost=$0.03 or 3 cents!

Kirchoff’s Rules

Rule #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

-6 v-2 v

-4 v

+12 v

example

3 A

5 A

2 A

10 A

example

Series CircuitsA series circuit has only one pathway around the circuitRule # 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:

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Series Christmas Tree Lights

Series wiring was often used for Christmas tree lights

When the bulb burns out, the jumper now has 120 volts across it.

One bulb burns out, they all go out! Who’s to say which one burned out!

Modern bulbs use a “jumper” wire. This wire has insulation around it.

The voltage produces a spark, and the insulation burns off. The circuit is now complete, with the one bulb not lit but easily replaced.

Parallel CircuitsA parallel circuit has multiple pathways around the circuitRule # 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:

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Combination Circuits

10 Ω 2 Ω

4 Ω2 Ω 4 Ω

1 Ω 120 V

2 Ω 4 Ω

1 Ω 120 V

??

??

4 Ω2 Ω 4 Ω

1 Ω 120 V

120 V

??

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

12 Ω

4 Ω2 Ω 4 Ω

1 Ω 120 V

2 Ω 4 Ω

1 Ω 120 V

3 Ω

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1Req

=1

12+

14

Req = 3 Ω

120 V

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.

120 V

10 Ω

I = ??

Find current through circuit

Find voltage across 3 Ω equivalent

Find current through 12 Ω equivalent

Find voltage across 2 Ω resistor

12 Ω

4 Ω2 Ω 4 Ω

1 Ω 120 V

A

10 Ω 2 Ω

4 Ω2 Ω 4 Ω

1 Ω 120 V

V

2 Ω 4 Ω

1 Ω 120 V

3 Ω

V