electric current and circuits presentation 2003 r. mcdermott
TRANSCRIPT
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