Electric Current and Electric Current and CircuitsCircuits

Presentation 2003 R. McDermott

What is Current?What is Current?

Electric current is a flow of electric chargeBy convention from + to –Actually electrons flow away from – and

toward +Current doesn’t slow down, nor does it get

“used up” Symbol of current is IUnit is the ampere (A)

Current is Flow of Charge in a Current is Flow of Charge in a ConductorConductor

I = Q/t

Example: A steady current of 4.0 amperes flows in a wire for 3 minutes. How much charge passes through the wire?

Answer: 720 C

Current Flows in an Electric Current Flows in an Electric CircuitCircuit

A continuous conducting path is called a circuit

Current flows through the

wires from one terminal

of the battery to the other

Current Doesn’t Flow in an Current Doesn’t Flow in an Open CircuitOpen Circuit

A wire with a break in the conducting path is called an open circuit

Since no current can exit

the wire, none can enter the

wire either – no current flow

Unscrewing a bulb creates an open circuit

What Really HappensWhat Really Happens

Potential difference of the battery sets up a non-uniform charge distribution on the surface of the wire

That produces an electric field in the wire

Free electrons leave negative terminal of battery, pass through circuit and re-enter battery at positive terminal

BatteriesBatteries

Batteries produce charge continuously from chemical reactions

Consist of two dissimilar metals in an electrolyte (liquid, paste, or gel)

Ohm’s LawOhm’s Law

Current flow is proportional to voltage Inversely proportional to resistance Resistance is constant of proportionality

V = I R I = V/R R=V/I

V

I R

Ohm’s Law V = IROhm’s Law V = IR

What happens to current if you increase V?What happens if you increase R?

I

V

Graph?

UNITSUNITS

Voltage Volt (V) Current Amperes (A) Resistance Ohm()

ResistanceResistance Since wires are filled with atoms, there will be

collisions and therefore resistance to the flow of current

The resistance increases with wire length and temperature, but decreases as the wire gets “fatter” (increased cross-sectional area)

As current flows through resistance, energy is removed (just like friction)

ResistanceResistance You can think about current as being like students

moving through a filled hallway:

– No one enters until someone leaves at the other end

– The length and width of the hallway affect the resistance to student walking

ResistanceResistance

Resistance of a metal wire:

R = L/A is resistivity

L is length of wireA is cross-sectional area

Silver has lowest resistivityCopper is almost as lowGold and Aluminum low too

SuperconductivitySuperconductivity

Resistance of certain materials

becomes zero at low temperatures Niobium-titanium wire at 23K Yttrium-Barium-Copper-Oxygen at 90K Bismuth-strontium-calcium copper oxide Can make strong electromagnets that do not

require power Japanese Maglev Train goes 329 mph

AC - DCAC - DC

DC is direct current.– Steady, one direction– Comes from battery or power supply

AC is alternating current– Back and forth– Sine wave with frequency of 60 Hz– House current

Electric PowerElectric Power

Power = energy transformed/time = QV/t P = IV unit: watt Since V = IR P = IV = I2R = V2/R

Which is more important,current or voltage?

In power transmission, why is high voltage advantageous?

Batteries in SeriesBatteries in Series

When batteries or other sources of potential are connected in series, the total potential difference is the algebraic sum of the separate potentials.

6V + 6V = 12V

Another example: a 9 volt radio battery consists of 6 1.5 volt cells in series.

Batteries in ParallelBatteries in Parallel

The voltages do not add, but current can be drawn for a longer time (more chemicals)

Circuit PotentialCircuit Potential

The battery produces a difference in “electrical height” from one end of the circuit to the other

Current (conventional) then flows “downhill” from the positive terminal to the negative

In a circuit, the potential difference is often referred to as the Electromotive Force, or EMF.

Circuit PotentialCircuit Potential

The diagram to the right illustrates the point:

The + terminal is the top of

the electrical hill

The - terminal is the bottom

of the electrical “hill”

Series Resistive CircuitSeries Resistive Circuit Full current goes through all circuit

components

Series Theory:Series Theory: The current must travel at the same speed

throughout the circuit ( I1 = I2 etc)

Normally, a “drop” would produce an increase in speed, but the energy of the “drops” is removed by the resistors

Theory:Theory:

Note that the drop heights (voltage drops) do not have to be equal

But they do have to add up to the total drop, so that Vt = V1 + V2

Theory:Theory:

In this diagram, resistor two has greater resistance, removes greater energy, and causes a greater potential drop than does resistor one

A resistor’s effects are proportional to its resistance

Theory:Theory:

Adding a 3rd resistor:

– The total potential drop is a fixed value– Resistor three has to take some of the total drop– Resistors one and two now have smaller potential drops

Theory:Theory:

Another point of view:

– Adding resistor three increases circuit resistance

since current must now pass through three resistors– Increased resistance decreases circuit current– Less current means less potential drop for resistors one

and two (and less energy)

Circuit DiagramsCircuit Diagrams A circuit diagram consists of symbols that represent

circuit elements:

Battery:

Resistor:

Rheostat:

Capacitor:

Switch:

Series DiagramSeries Diagram

This is the circuit diagram for our two- resistor series circuit

Series DiagramSeries Diagram

And this one is our three-resistor series circuit

Series Sample #1Series Sample #1

– Which direction does current flow?

– Find total resistance– Find circuit current

– Find V1 and V2

– Find circuit power

– Find P1 and P2

Series Sample #1: Series Sample #1:

Circuit resistance in a series circuit is:

Rc = R1 + R2

Rc = 2 + 4

Rc = 6

Circuit current in a series circuit is:

Ic = Vc/Rc

Ic = 12v/6

Ic = 2a

Sample #1: Sample #1:

The voltage drop in resistor one obeys Ohm’s Law:

V1 = I1R1

V1 = (2a)(2)

V1 = 4v

As does the voltage drop in resistor two:

V2 = I2R2

V2 = (2a)(4)

V2 = 8v

Sample #1: Sample #1: Since we know the circuit current and the circuit

voltage, power is best found by: Pc = IcVc • Pc = (2a)(12v)• Pc = 24w

For the resistors, however, it might be a bit safer to choose the equation: P = I2R

P1 = I12R1 and P2 = I2

2R2

P1 = (2a)2 2 P2 = (2a)24

P1 = 8w P2 = 16w

Ratios?Ratios?

In a series circuit, ratios can be used if you’re very careful

The resistances, voltage drops, and power are directly proportional:

R1 = 2 R2 = 4 Rc = 8

V1 = 4v V2 = 8v Vc = 12v

P1 = 8w P2 = 16w Pc = 24w

Series Sample #2Series Sample #2

– Which direction does current flow?

– Find total resistance– Find circuit current

– Find V1 ,V2 and V3

– Find circuit power

– Find P1 ,P2 and P3

Parallel Resistive CircuitParallel Resistive Circuit

Same voltage across all circuit elements

IT = I1 + I2 + I3 +

V/RT = V/R1 + V/R2 + V/R3

1/RT = 1/R1 + 1/R2 + 1/R3 +

Parallel Theory:Parallel Theory:

In a circuit, the total potential difference supplied by the battery is fixed

To the right, each branch goes from the top of the battery to the bottom

Therefore each potential drop

is equal: Vt = V1 = V2

Theory:Theory:

To the right, the current splits

at the first junction, and then

recombines at the second

The total current can’t change:

It = I1 + I2

The current dos not have to divide equally; the branch with less resistance gets more of the current

Theory:Theory:

Follow-up explanation:

Each branch has the same

voltage

I = V/R

So the branch with less resistance gets more of the current

Theory:Theory:

Two or more paths to follow

Effectively makes the wire

thicker (cross-sectional area)

More total current can flow

So the more parallel paths (resistors), the less the total resistance of the circuit must be!

In fact, the total resistance will always be less than the smallest resistor in the parallel combination.

Theory:Theory:

If resistor two has a greater

resistance than resistor one:

It will draw less current

and power than resistor one

But they have the same voltage

In a parallel circuit, a resistor’s effects are inverse to the size of the resistor

Theory:Theory:

Adding a 3rd resistor:

– Resistors one and two get same voltage as before, therefore the same current and power

– Resistor three has full battery voltage, so draws additional current from battery

– Total circuit current and power rises– Adding (or removing) a resistor has no effect on other

resistors

Parallel DiagramParallel Diagram

This is the circuit diagram for our two resistor parallel circuit

Parallel DiagramParallel Diagram

And this one is our three resistor parallel circuit

Parallel Sample #1Parallel Sample #1

– Find the total resistance and total circuit current

– Find I1 and I2

– Find V1 and V2

– Find circuit power

– Find P1 and P2

Parallel Sample #1: Parallel Sample #1: The total circuit resistance can found by using:

the equation: 1/Rc = 1/R1 + 1/R2 + …

1/Rc = ½ + ¼ = ¾ Rc = 4/3 = 1.33

The circuit current by: Ic = Vc/Rc Ic = (12V)/(1.33 ) Ic = 9a

Parallel #1: Parallel #1:

I = V/R

I1 = 12V/2 I1 = 6a

I2 = 12V/4 I2 = 3a

P = V2/R

Pc = (12v)2/(1.33)

Pc = 108w

P1 = (12v)2/(2)

P1 = 72w

P2 = (12v)2/(4)

P2 = 36w

Ratios?Ratios?

In a parallel circuit, ratios can be used if you’re very careful

The current and power are inversely proportional to the resistance:

R1 = 2 R2 = 4 Rc = 1.33

I1 = 6a I2 = 3a Ic = 9a

P1 = 72w P2 = 36w Pc = 108w

Parallel Sample #2Parallel Sample #2

– Find the total resistance and total circuit current

– Find I1 , I2 and I3

– Find V1 ,V2 and V3

– Find circuit power

– Find P1 , P2 and P3

Capacitors in SeriesCapacitors in Series

Charge same on each capacitorQ = CTV

V = V1 + V2 + V3

Q/CT = Q/C1 + Q/C2 + Q/C3

1/CT = 1/C1 + 1/C2 +1/C3

Capacitors in ParallelCapacitors in Parallel

Total charge is sum of charges on individual capacitors

Q = Q1 +Q2 + Q3 = C1V +C2V + C3V

Q = CTV

CTV = C1V +C2V + C3V

CT = C1 + C2 + C3

Short-CircuitShort-Circuit An electrical short occurs when a low-resistance alternate

path for current exists. In this case, current will completely bypass anything connected between the two points that are shorted. In the diagram below, the short from A to B cuts off current flow to resistor 1, but not resistor 2.

Capacitor BehaviorCapacitor Behavior When a capacitor is charging, it acts like a short circuit,

drawing all the current When it is finished charging, it acts like an open circuit

When the switch is closed, the

current bypasses the resistor As the capacitor charges, the

resistor begins to get current Once the capacitor is fully

charged, current flows only to

the resistor

AcknowledgementsAcknowledgements

Graphics and animation courtesy of Tom Henderson, Glenbrook South High School, Illinois

Graphics courtesy of Dr. Phil Dauber