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Electric Current and Circuits

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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
- Unit is the ampere (A)

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

- 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

- 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

- 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 produce charge continuously from chemical reactions
- Consist of two dissimilar metals in an electrolyte (liquid, paste, or gel)

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

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

I

Graph?

V

UNITS

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

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)

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

- No one enters until someone leaves

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

- 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

- 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

- 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

- 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

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

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 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

Full current goes through all circuit components

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:

- 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:

- 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:

- 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:

- 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)

- Adding resistor three increases circuit resistance

Circuit Diagrams

- A circuit diagram consists of symbols that represent circuit elements:
- Battery:
- Resistor:
- Rheostat:
- Capacitor:
- Switch:

Series Diagram

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

Series Diagram

And this one is our three-resistor series circuit

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

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: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: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? 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 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 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: 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

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

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

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.

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

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 power is best found by: Pc = IcVc

This is the circuit diagram for our two resistor parallel circuit

Parallel Diagram power is best found by: Pc = IcVc

And this one is our three resistor parallel circuit

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

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: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: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 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 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 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 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 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 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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