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ReviewAn electric circuit is composed of what 3 elements?
• Conductor, potential difference, closed loop
What are the units of voltage?•Joules / Coulomb•Electric potential energy / unit charge
Current?•Amperes / second•A flow of charged particles•
Resistance?•Ohms
Current• Electric current is the rate of flow of charge
• I = Δq/ Δt
• Ampere = Coulomb per second (passing by a point in a circuit)
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.
Ohm’s Law Mnemonic
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)
Changing Temperature
Questions
What is the effect on the current through a system if the voltage is doubled? Resistance doubled? Both?
A device connected to a 1.5V battery conducts a drives a 45x10-6 A current, while the same device connected to a 3V battery conducts a 90x10-3 A current. Is the device ohmic?
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)
• Power = Work / time
• Electrical Energy = Power * Time = IV * t
Electrical Power
• P= IV “Poison Ivy”
Electrical Power
• P= IV = I2R = V2/R
Electrical Power
• Electrical Power is priced in kWh– One kiloWatt = 1000 Watts– One kWh = One kW for one hour
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
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
Diagramming circuits
Kirchoff’s Junction Rule
• Conservation of charge
Kirchoff’s Loop Rule• Conservation of Energy
• The sum of the changes in potential around any closed path (loop) of a circuit must be zero.
R2
A
R1 +
V
Series Circuit
• Current : One path for the flow of charge
• It=I1=I2=I3
• Resistance must increase because length increases
• Rt-=R1+R2+R3
• Voltage must add to Zero
• Vt-V1-V2-V3=0 Vt=V1+V2+V3
Series and Parallel Circuits
• What does it mean to go in series?– Single file
• What does it mean to go in parallel?– Multiple paths
Series Circuit:
– ammeters are always in the circuit, they measure flow of charge
• Ammeters should always have low resistance– Otherwise they will affect the measurement by adding resistance
R2
A
R1 +
V
Series Circuit Example
R3
A
V1, I1
+
IT
VV
VV
V3, I3
R1 VT
Given:
Vt = 10V
R1 = 5
I2 = 1A
P3 = 2W
R2 VV V2, I2
Vt = 10V V1 = V2 = V3 =
It = I1 = I2 = 1A I3 =
Rt = R1 = 5 R2 = R3 =
Pt = P1 = P2 = P3 = 2W
Series Circuit Example
R3
A
V1, I1
+
IT
VV
VV
V3, I3
R1 VT
Given:
Vt = 10V
R1 = 5
I2 = 1A
P3 = 2W
R2 VV V2, I2
Vt = 10V V1 = 5V V2 = 3V V3 = 2V
It = 1A I1 = 1A I2 = 1A I3 = 1A
Rt = 10 R1 = 5 R2 = 3 R3 = 2
Pt = 10W P1 = 5W P2 = 3W P3 = 2W
Series and Parallel Circuits
a
L
A
L
Parallel: Multiple Paths, low effective resistance
Series: Single Path, high effective resistance
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 charges have the same drop
R3 V2
A
VV
IT
R1
IT
R2 VVVV V3V1
Parallel Circuit: •Voltmeters are parallel to the circuit, they measure the potential•Voltmeters should always have high resistance
•Otherwise they will allow current to flow through them and reduce effective resistance
I1
I2 + I3
IT
IT = I1 + I2 + I3 by Conservation of charge (conservation of matter)
Parallel Equations• It = I1 + I2 + I3 + …
So
• It/Vt = I1/Vt + I2/Vt + I3/Vt …
But
• Vt = V1 = V2 = V3 =, implying
• It/Vt = I1/V1 + I2/V2 + I3/V3 …
Or, by Ohm’s law,
• 1/Rt = 1/R1 + 1/R2 + 1/R3 + …
Parallel Equations
AIT
R1
IT
R2
Parallel Circuit: •Follow the current•If R1 > R2 > R3, what will the relationship between I1, I2, and I3 be? V1, V2, V3?
V1, I1V3, I3
V2, I2
R3
Circuit 1
AIT
R1
VT
R2
Parallel Circuit: •Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2, find the other values associated with this circuit.
V3, I3
V2, I2
R3 V1, I1
Vt = V1 = V2 = V3 =
It = I1 = 3A I2 = I3 =
Rt = R1 = 3 R2 = R3 = 2
Pt = P1 = P2 = 18W P3 =
AIT
R1
VT
R2
Parallel Circuit: •Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2, find the other values associated with this circuit.
V3, I3
V2, I2
R3 V1, I1
Vt =9V V1 = 9V V2 =9V V3 =9V
It =9.5A I1 = 3A I2 =2A I3 =4.5A
Rt =0.95 R1 = 3 R2 =4.5 R3 = 2
Pt =85.5W P1 = 27W P2 = 18W P3 = 40.5W
Series Circuit Example: Voltage Divider
A
V1, I1+
IT
VVR1 VT
Given:
Vt = 24V
Choose values of R1 and R2 to
produce 20V across R2
R2 VVV2, I2
Vt =24V V1 =4 V2 =20
It = I1 = I2 =
Rt = R1 = R2 =
Pt = P1 = P2 =
Series Circuit Example: Voltage Divider
A
V1, I1+
IT
VVR1 VT
Given:
Vt = 24V
Choose values of R1 and R2 to
produce 20V across R2
R2 VVV2, I2
Vt =24V V1 =4 V2 =20
It = 1A I1 = 1A I2 = 1A
Rt = 24 R1 = 4 R2 =20
Pt =24W P1 = 4W P2 = 20W
AIT
R1
VT
R2
Series / Parallel Circuit: •Given V4=12, I1 = 3A, R2= 2, R3=3, P3 = 18W. Find the other values.
V3, I3
V2, I2
R3
V4, I4
V1, I1
R4
Vt = V1 = V2 = V3 = V4 =12V
It = I1 = 3A I2 = I3 = I4 =
Rt = R1 = R2 =2 R3 =3 R4 =
Pt = P1 = P2 = P3 = 18W P4=
AIT
R1
VT
R2
Series / Parallel Circuit: •Given V4=12, I1 = 3A, R2= 2, R3=3, P3 = 18W. Find the other values.
V3, I3
V2, I2
R3
V4, I4
V1, I1
R4
Vt =19.34V V1 =7.34V V2 =7.34V V3 =7.34V V4 =12V
It =9.12A I1 = 3A I2 =3.67A I3 =2.45 I4 =9.12A
Rt =2.12 R1 = 2.45 R2 =2 R3 =3 R4 = 1.31
Pt =176.4W P1 =22W P2 =26.94W P3 = 18W P4=109.4W