ohm’s law objective: tsw understand the concepts of voltage, current, and resistance by developing...
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Ohm’s Law
Objective:
TSW understand the concepts of Voltage, Current, and Resistance by developing and applying Ohm’s Law.
Circuit simulation
R
V
II
I
I
I
I
I
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)
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 IPredict the current with a small voltage and a large resistance:
RandV 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 R IA small voltage (V) with a large resistance (R) results in a small current (I).
RandV I
I =VR
= IV
R
=IVR
This equation can be rearranged to form Ohm’s Law:
R
VI
IRV
Here are some graphs that represent the relationship:
V
I
R IRV
I
R
R
VI
When we talk about electricity we often refer to the quantity power.
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).
IVP
Power is the rate at which energy is used. Units: (J/s =Watt)
Check out the units:
C
J
s
C)(WWatt
s
J
The power equation can be combined with Ohm’s Law to give several variations in order calculate the power.
IVP
RIP
IRIP2
)(
IRV IVP
IR
V
R
VP
VR
VP
2
)(
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?
AI
I
IVP
5.0
)120(60
240
)5.0(120
R
R
IRV
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.
AI
I
IRV
1
)240(240
WP
P
IVP
240
)240)(1(
Resistance of a wire
A
LR
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+...
is RR
R2
R3
24V
R1
I
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
Series CircuitR1=3Ω
R2 =
5Ω
R3=4Ω
24V
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
Series CircuitR1=2Ω
R2 =
3Ω
R3=5Ω
12V
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
Series CircuitR1=10Ω
R2 =
8Ω
R3=12Ω
48V
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+ …
ip RR
11
R1
R312V
R2 I3
I2I1
I
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
Parallel Circuit
R1 =
5Ω
R3 =
10Ω12V
R2 =
2Ω
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
Parallel Circuit
R1 =
3Ω
R3 =
4Ω24V
R2 =
8Ω
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
Parallel Circuit
R1 =
10Ω
R3 =
20Ω50V
R2 =
15Ω
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 I P
Batt
R1
R2
R3
R2 =
4Ω
R1=4Ω
R3 =
4Ω12V
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
R2 =
2ΩR
1 =4Ω
R3 =
3Ω12V
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
R2 =
1ΩR
1 =3Ω
R3 =
8Ω15V
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
R2 =
3Ω
R1=2Ω
R3 =
5Ω24V
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
R4
R1=2Ω
R3 =
1Ω
28V R4 =
2Ω
R2 =
3Ω
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
R4
R1=4Ω
R3 =
2Ω30V
R2 =
6Ω
R4=2Ω
Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.
V I P
Batt
R1
R2
R3
R4
R5
R1=4Ω
R5 =
6Ω26V
R2 =
3Ω
R4 =
1ΩR
3 =2Ω
The circuit below has been connected for a long time such that all currents have reached their steady states.
R1=1000Ω
12V
R2 =
500Ω
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.
+-
εri
terminal voltage
Example: The ammeter reads 0.5A. What is the emf of the battery? What is the terminal voltage across X and Y?
10Ω
14Ωε
internal resistance
2Ω
X
YA
Ammeters must be connected in series and ideally have zero resistance.
R1
R2
ε
A
Voltmeters must be connected in parallel and ideally have infinite resistance.
R1
R2
ε
V