Download Circuits - Wappingers Central School District

Electrical Circuits
An electric circuit is composed of 3 elements
•
Conductor, potential difference, closed loop
•
An electrical circuit without a load that has
some resistance is essentially a short circuit
•(Think about the batteries in the simulation)
•(An ammeter has very little resistance. Think
about my poor ammeters in a circuit with no
loads or other resistance.)
Electrical Circuits
In a series electric circuit all of the electrons must flow
through the same elements
In a parallel electric circuit electrons may flow through
different circuit elements
Electrical Circuits
In a series electric circuit, the voltage drops as it flows
through each resistive circuit element
Resistors in Series: Building Analogy
R1 = Lamp
R1
Elevator
R2 = Lamp
(battery)
R3 = Lamp
R2
3 steps
To go from the top to the bottom floor, all people must take the same path. So,
by definition, the staircases are in series. With each flight people lose some of
the potential energy given to them by the elevator, expending all of it by the
time they reach the ground floor. So the sum of the V drops across the resistors
the voltage of the battery. People lose more potential energy going down longer
flights of stairs, so long stairways correspond to high resistance resistors.
The double waterfall is like a pair of resistors in series because there is only one
route for the water to take. The longer the fall, the greater the resistance.
Diagramming circuits
Ohm’s Law: Ohm's Law …says that, for many
materials under a wide range of conditions, the
voltage, V, and current, I, are linearly related, which
implies resistance, R, is independent of V and I.
When does it not apply? (Most important case)
Ohm’s Law Mnemonic
Resistance and Ohm’s Law
• Resistance is the impedance to the flow of
charge
• Resistance is defined as the ratio of
potential difference to current
• R = V/I Unit is the Ohm, Ω
• A device is said to obey Ohm’s Law of its
resistance is independent of the Voltage
First, fill in all values of V and I.
After review, fill in values of R
I1 = 1
A
V1 = 9
+
V
V2 =
R2 =
First, fill in all values of V and I.
After review, fill in values of R
I2 =
A
V3 =
+
V
V4 =
R4 =
A
I3 = 2
V
V5 = 2
R5 =
First, fill in all values of V and I.
After review, fill in values of R
I4 = 1
A
V6 =
+
V
V7 =
R7 =
A I5 =
V
V8 = 3
R8 =
V9 =
R9 =
A I6 =
V
We will work this one out together
I4 =
A
V6 =
+
V
V7 =
R7 = 1
V
V7 =
R7 = 2
A I5 =
V
V8 = 6
R8 = 3
V9 =
R9 = 4
A I6 =
V
We will work this one out together
I4 =
A
VT = V1 + V2 + V3 + …
V
V7 =3
R7 =
V
V8 =
R8 = 2
RT = R1 + R2 + R3 + …
V6 =
+
A I5 =
IT = I1 = I2 = I3 = …
V
V9 = 5
R9 =
V10 =4
R10 = 4
A I6 =
V
Questions
What happens if we greatly increase the
resistance?
When else, besides electricity, do we see
things like this?
- Think about the effects on voltage
(pressure), current (flow), and resistance
(blockage)
Tell me about heart
bypassess…
Tell me about heart
bypassess…
Parallel Circuit
• More than one path for the flow of charge
• More room for the flow of charge so
Resistance goes down
• Voltage must stay the same since all
sections have the same drop
Parallel Circuit:
•Voltmeters are parallel to the circuit
How do the sum of I1,
I2, and I3 relate to IT?
IT
IT
I2 + I3
A
Hint: What is current?
What is it made up of?
I1
R1
IT A
V V1
A
A
R2
R3
V V2
A
V V3
Parallel Circuit:
•Voltmeters are parallel to the circuit
IT
IT
I2 + I3
A
IT = I1 + I2 + I3 by
Conservation of charge
(conservation of
matter)
I1
R1
IT A
V V1
R2
V V2
R3
V V3
Parallel Circuit:
•Follow the current
•Now map the current flow for circuit 2
IT
A
A
R4
R1
V1, I1
R2
V2, I2
R3
R5
R6
V3, I3
IT A
Circuit 1
Circuit 2
Parallel Circuit:
•Follow the current
•How does circuit 1 differ from circuit 2?
IT
A
A
R4
R1
IT A
V1, I1
R2
V2, I2
R3
V3, I3
R5
R6
VT = 120V
V1 =
V2 =
R1 =
100 Ohms
R2 =
200 Ohms
VT
RT =
R1
IT A
IT =
I1 =
I2 =
V1, I1
R2
V2, I2
V
R1 =
100 Ohms
R2 =
200 Ohms
R3 =
150 Ohms
VT = 120V
V1 =
V2 =
VT
RT =
V3 =
R1
IT A
IT =
I1 =
I2 =
I3 =
V1, I1
R2
V2, I2
R3
V3, I3
V
R1 =
VT = 120V
Rwire = 1 Ohms
V1 =
V2 =
R2 =
R3 =
VT
RT =
V3 =
R1
IT A
IT =
I1 = 5A (600W)
I2 = 5A
I3 = 5A
V1, I1
R2
V2, I2
R3
V3, I3
V
1 / RT  1 / R1  1 / R2  1 / R3 ...
Resistance of an object
• What would we expect it to depend on?
• (Resistance is the impedance to the flow
of charge)
Resistance of an object
• What would we expect it to depend on?
• (Resistance is the impedance to the flow
of charge)
A
Find Resistance of a material
• Depends on four factors
– R ∞ Temp
– R ∞ RHO (ρ) resitivity
– R ∞ Length
– R ∞ A-1 (cross-sectional Area)
Low resistance
• Short
• Fat
• cold
High Resistance
• Long
• Thin
• Hot
Series and Parallel Circuits
a
A
Resistivities at 20°C
Material
Resistivity
Aluminum
2.82 × 10–8
Copper
1.72 × 10–8
Gold
2.44 × 10–8
Nichrome
150. × 10–8
Silver
1.59 × 10–8
Tungsten
5.60 × 10–8
From Reference tables
Electrical Power
• P= IV “Poison Ivy”
Electrical Power
• Power is the rate at which work is done or
energy is expended.
– Unit is Watt = Joule / second
– (James Watt worked on steam engines and launched
the industrial revolution)
• Electrical Energy = Power * Time = VIt
Electrical Power
• Electrical Power is priced in kWh
– One kiloWatt = 1000 Watts
– One kWh = One kW for one hour
Monthly Service Charge is $18
Central Hudson Variable Costs
$0.047
$0.002
-$0.007
$0.004
$0.001
$0.003
$0.001
$0.004
$0.065
$0.014
Total
$0.134
Monthly Charges
–
$6.00
Basic Charge, plus
$0.06850 per Kwh for the first
600
$0.07933 per Kwh for the next
700
per Kwh for all additional
$0.09260 Kwhs
(Includes the
effect of
Schedules
59, 91, & 93)
Kwhs
Kwhs
Example If you
Kwhs of electricity, your bill would be calculated
used 1450 like this:
Basic
Charge
=
$6.00
$0.06850
x
600
Kwhs =
$41.100
$0.07933
$0.09260
x
x
700
150
Charge for 1450 Kwhs
Kwhs
Kwhs
=
=
=
$55.531
$13.890
(franchise fees not
$116.52included)