Download 3. DC Circuits

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)
Ohm’s Law

Current flow is proportional to voltage
 Inversely proportional to resistance
 Resistance is constant of proportionality
V=IR
 I = V/R
 R=V/I

V
I
R
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
Resistance

Resistance of a metal wire:
R = rL/A r 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)
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 tworesistor 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
Series Sample #1:

Circuit resistance in a
series circuit is:

Circuit current in a
series circuit is:

Rc = R1 + R2

Ic = Vc/Rc

Rc = 2 + 4

Ic = 12v/6

Rc = 6

Ic = 2a
Sample #1:

The voltage drop in
resistor one obeys
Ohm’s Law:

As does the voltage
drop in resistor two:

V 1 = I 1R 1

V2 = I2R2

V1 = (2a)(2)

V2 = (2a)(4)

V1 = 4v

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
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
V1 = 4v
P1 = 8w
R2 = 4
V2 = 8v
P2 = 16w
Rc = 8
Vc = 12v
Pc = 24w
Series 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 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:

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:

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:

Follow-up explanation:

Each branch has the same
voltage

I = V/R

So the branch with less resistance gets more of the
current
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:

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:

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
This is the circuit
diagram for our two
resistor parallel circuit
Parallel Diagram
And this one is our
three resistor parallel
circuit
Parallel 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:

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:





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?

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
– 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

Charge same on each capacitor
 Q = CTV
 V = V1 + V 2 + V 3
 Q/CT = Q/C1 + Q/C2 + Q/C3
 1/CT = 1/C1 + 1/C2 +1/C3
Capacitors 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-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 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
Acknowledgements

Graphics and animation courtesy of Tom
Henderson, Glenbrook South High School,
Illinois
 Graphics courtesy of Dr. Phil Dauber