Transcript Ohm`s Law and Circuit Analysis

Ohm’s Law
Objective:
TSW understand the concepts of Voltage,
Current, and Resistance by developing and
applying Ohm’s Law.
Circuit simulation
R
I
I
I
I
I
I
V
V = Voltage = A potential difference that motivates
charge to flow. The pump. (units: V = J/C)
I = current = The amount of charge that flows per
unit time. (units: C/s = Amps A)
R = Resistance = A property of the material that
resists the flow of current. (units: Ohms Ω = V/A)
I
Let’s learn how these three quantities are related
by imaging different Voltages with a constant
Resistance.
Predict the current with a large voltage and a small resistance:
V
and
R
I
Predict the current with a small voltage and a large resistance:
V
and
R
I
Let’s come up with an equation for the current (I)
that related to the Voltage (V) and Resistance (R):
A large voltage (V) with a small resistance (R) results in a large
current (I).
V
and
V =I
I
R
R
A small voltage (V) with a large resistance (R) results in a small
current (I).
V
V
and
R
I
I=
R
V
R
=I
This equation can be rearranged to form Ohm’s Law:
V
I
R
Here are some graphs that represent
the relationship:
V
V  IR
V  IR
R
I
I
V
I
R
R
When we talk about electricity we often refer to the
quantity power.
Power is the rate at which energy is used. Units: (J/s =Watt)
Let’s define power as it relates to an electrical circuit.
The power is large when a large voltage (V) is used to
produce a large current flow (I).
P  IV
Check out the units:
J
 C  J 
     Watt (W )
 s  C 
s
The power equation can be combined with Ohm’s Law to
give several variations in order calculate the power.
P  IV
P  I ( IR )
PI R
2
V  IR
P  IV
V
I
R
V
P  (V )
R
2
V
P
R
Example 1: A 60W/120V light bulb is connected to a 120V power supply.
What is the resistance of the light bulb and the current flowing in the circuit?
P  IV
V  IR
60  I (120)
I  0.5 A
120  (0.5) R
R  240
The same 60W/120V light bulb is connected to a 240V power supply. What will
be different from the calculations above?
Since resistance is a property of the light bulb it will be the same as above,
but the current and power of the bulb will be greater.
V  IR
240  I (240)
I  1A
P  IV
P  (1)( 240)
P  240W
Resistance of a wire
R
L
A
R = Resistance (ohms Ω)
ρ = resistivity (Ωm) depends of the material
the wire is made from.
A = cross sectional area (m2)
A
L
Circuit Analysis
Objective: TSW apply voltage, current and
resistance to predict the behavior of various
circuits by completing a VIP chart.
Series Circuit
•
•
•
•
•
Current is the same.
Voltage is split.
When one bulb goes out, all go out
Greatest resistance is the brightest.
Rs=R1+R2+R3+...
R2
Rs   Ri
R1
24V
I
R3
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
Series Circuit
V
R1=3Ω
R2=5Ω
24V
R3=4Ω
Batt
R1
R2
R3
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
Series Circuit
V
R1=2Ω
R2=3Ω
12V
R3=5Ω
Batt
R1
R2
R3
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
Series Circuit
V
R1=10Ω
R2=8Ω
48V
R3=12Ω
Batt
R1
R2
R3
I
P
Parallel Circuit
•
•
•
•
•
Voltage is the same.
Current is split.
When one bulb goes out, others stay the same.
Least resistance is the brightest
1/Rp=1/R1+1/R2+1/R3+ …
I3
R3
I
I2
R2
I1
12V
R1
1
1

Rp
Ri
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
Parallel Circuit
R3=10Ω
R2=2Ω
R1=5Ω
12V
V
Batt
R1
R2
R3
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
Parallel Circuit
R3=4Ω
R2=8Ω
R1=3Ω
24V
V
Batt
R1
R2
R3
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
Parallel Circuit
R3=20Ω
R2=15Ω
R1=10Ω
50V
V
Batt
R1
R2
R3
I
P
Combined Circuits
• Map the currents. Currents divide at junctions
• Find the total resistance. Start with resistors in series.
• Resistors in series have the same current flowing
through them.
• Resistors in parallel have the same voltage (potential
difference)
• Use Ohm’s law to find the main current.
• Use the loop rule to find the voltage (potential difference)
across individual resistors.
• Use proportional thinking to find the current flowing
through individual resistors.
• Complete the VIP chart.
• Check: The power of individual resistors should always
add to the power of the battery.
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
V
R1=4Ω
R3=4Ω
R2=4Ω
12V
Batt
R1
R2
R3
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
V
R3=3Ω
R1=4Ω R2=2Ω
12V
Batt
R1
R2
R3
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
V
R3=8Ω
R1=3Ω R2=1Ω
15V
Batt
R1
R2
R3
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
V
R1=2Ω
R3=5Ω
R2=3Ω
24V
Batt
R1
R2
R3
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
V
R1=2Ω
R3=1Ω
R4=2Ω
R2=3Ω
28V
Batt
R1
R2
R3
R4
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
V
R1=4Ω
R4=2Ω
R3=2Ω
R2=6Ω
30V
Batt
R1
R2
R3
R4
I
P
Each resister represents a light bulb. Complete the VIP chart
in order to rank the brightness of the bulbs.
V
R1=4Ω
R5=6Ω
R3=2Ω
R2=3Ω
26V
R4=1Ω
Batt
R1
R2
R3
R4
R5
I
P
The circuit below has been connected for a long time such
that all currents have reached their steady states.
R1=1000Ω
R2=500Ω
12V
30x10-6F
Calculate the current in the 500Ω resistor.
Calculate the charge stored in the capacitor.
Calculate the power dissipated in the 1000Ω.
Internal Resistance – The resistance due to
the battery or power supply
A battery consists of a EMF (ε) and an internal resistance.
The potential difference across the terminals is called the
terminal voltage.
-
+
ri
ε
terminal voltage
Example: The ammeter reads 0.5A. What is the emf of the
battery? What is the terminal voltage across X and Y?
X
10Ω
ε
14Ω
internal
resistance
2Ω
A
Y
Ammeters must be connected in series and ideally have zero
resistance.
R1
ε
R2
A
Voltmeters must be connected in parallel and ideally have
infinite resistance.
R1
ε
V
R2