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Electric Current and Circuits. Presentation 2003 R. McDermott. What is Current?. Electric current is a flow of electric charge By 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 I

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Electric current and circuits

Electric Current and Circuits

Presentation 2003 R. McDermott


What is current
What is Current?

  • Electric current is a flow of electric charge

  • By 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 I

  • Unit is the ampere (A)


Current is flow of charge in a conductor
Current is Flow of Charge in a Conductor

  • I = DQ/Dt

  • 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 circuit
Current Flows in an Electric Circuit

  • 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 open circuit
Current Doesn’t Flow in an Open 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 happens
What 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


Batteries
Batteries

  • Batteries produce charge continuously from chemical reactions

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


Ohm s law

V

I

R

Ohm’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


Ohm s law v ir
Ohm’s Law V = IR

  • What happens to current if you increase V?

  • What happens if you increase R?

I

Graph?

V


Units
UNITS

  • Voltage Volt (V)

  • Current Amperes (A)

  • Resistance Ohm()


Resistance
Resistance

  • 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)


Resistance1
Resistance

  • 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


Resistance2
Resistance

  • Resistance of a metal wire:

    R = rL/Ar is resistivity

    L is length of wire

    A is cross-sectional area

    Silver has lowest resistivity

    Copper is almost as low

    Gold and Aluminum low too


Superconductivity
Superconductivity

  • 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 dc
AC - 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 power
Electric 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 series
Batteries 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 parallel
Batteries in Parallel

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


Circuit potential
Circuit 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 potential1
Circuit 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 circuit
Series 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


Theory1
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


Theory2
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


Theory3
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 diagrams
Circuit Diagrams

  • A circuit diagram consists of symbols that represent circuit elements:

    • Battery:

    • Resistor:

    • Rheostat:

    • Capacitor:

    • Switch:


Series diagram
Series Diagram

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


Series diagram1
Series Diagram

And this one is our three-resistor series circuit


Series sample 1
Series 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 11

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

Series 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 11

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 = I22R2

P1 = (2a)2 2 P2 = (2a)24

P1 = 8w P2 = 16w

Sample #1:


Ratios
Ratios? power is best found by: Pc = IcVc

  • 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 2
Series Sample #2 power is best found by: Pc = IcVc

  • 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 circuit
Parallel Resistive Circuit power is best found by: Pc = IcVc

  • 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: power is best found by: Pc = IcVc

  • 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


Theory4
Theory: power is best found by: Pc = IcVc

  • 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


Theory5
Theory: power is best found by: Pc = IcVc

  • Follow-up explanation:

  • Each branch has the same

    voltage

  • I = V/R

  • So the branch with less resistance gets more of the current


Theory6
Theory: power is best found by: Pc = IcVc

  • 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.


Theory7
Theory: power is best found by: Pc = IcVc

  • 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


Theory8
Theory: power is best found by: Pc = IcVc

  • 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 diagram
Parallel Diagram power is best found by: Pc = IcVc

This is the circuit diagram for our two resistor parallel circuit


Parallel diagram1
Parallel Diagram power is best found by: Pc = IcVc

And this one is our three resistor parallel circuit


Parallel sample 1
Parallel Sample #1 power is best found by: Pc = IcVc

  • 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 11

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 Sample #1:


Parallel 1

I equation: 1/Rc = 1/R= 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

Parallel #1:


Ratios1
Ratios? equation: 1/Rc = 1/R

  • 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 2
Parallel Sample #2 equation: 1/Rc = 1/R

  • 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 series
Capacitors in Series equation: 1/Rc = 1/R

  • Charge same on each capacitor

  • Q = CTV

  • V = V1 + V2 + V3

  • Q/CT =Q/C1 +Q/C2 + Q/C3

  • 1/CT = 1/C1 + 1/C2 +1/C3


Capacitors in parallel
Capacitors in Parallel equation: 1/Rc = 1/R

  • 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 circuit
Short-Circuit equation: 1/Rc = 1/R

  • 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 behavior
Capacitor Behavior equation: 1/Rc = 1/R

  • 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


Acknowledgements
Acknowledgements equation: 1/Rc = 1/R

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

  • Graphics courtesy of Dr. Phil Dauber


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