Transcript Document 7188053
What’s a Circuit?
A circuit is a closed path where positive charges flow from high to low potential energy. They can be manipulated on the way.
The Power Source
Provides the difference in potential (potential energy per unit charge). It is measured in volts (remember this) A Cell (battery) is the easiest to see. It converts chemical energy to electrical energy.
This is also called “Electromotive force” (or emf) Think of “Voltage” as “pressure” that causes charges to move.
What is
Electric Current
?
An electric current is the flow of electrons through wires and components.
The greater the current, the more charges are moving!
+ -
In which direction does the electrons flow?
It flows from the negative terminal to the positive terminal.
Measured in Amperes (we say Amps )
Conventional Current
+ + + e Electron flow Conventional flow + Electron flow: of e The direction flowing from – to +. Conventional current: The motion of +q from + to – has same effect.
Electric fields and potential are defined in terms of +q , so we will assume conventional current (even if electron flow may be the actual flow).
Electric Current
Electric current I is the rate of the flow of charge Q through a cross-section A in a unit of time t .
+ Wire
I
Q t
1 A 1C 1 s +Q A t One ampere A is charge flowing at the rate of one coulomb per second .
Resistance
When an object (like a light bulb) resists or diminishes the flow of current, it has resistance .
Resistance is measured in Ohms Symbol for Ohms: Ω
Factors Affecting Resistance
1. The length L of the material. Longer materials have greater resistance.
L 2L 1 W 2 W 2. The cross-sectional area A Larger areas offer LESS of the material. resistance.
2 W A 2A 1 W
Factors Affecting R (Cont.)
3. The temperature T higher temperatures usually result in higher resistances.
of the material. The R > R o R o 4. The kind of material . Iron has more electrical resistance than a geometrically similar copper conductor.
R i > R c Copper Iron
Resistivity of a Material
The resistivity r is a property of a material that determines its electrical resistance R .
Recalling that to length to area A L R is directly proportional and inversely proportional , we may write:
R
r
L A
or r
RA L
The unit of resistivity is the ohm-meter ( W m)
Water Analogy to EMF
High pressure Constriction Low pressure Water Flow Valve High potential + Resistor
R I
Low potential Switch
E
Water
Pump
Source of EMF The source of emf (pressure) to force electrons electric resistance (pump) provides the voltage (water) through (narrow constriction).
Ohm’s Law
Relates the voltage (Volts), current (Amps), and resistance (Ohms) in a circuit.
V
V = Voltage (in Volts) I = Current (in Amps) R = Resistance (in Ω)
IR
Ohmic Resistors
An
ohmic resistor
obeys Ohm’s law. A graph of voltage vs current gives a straight line with a positive slope. The steeper the slope, the higher the resistance will be.
Nonohmic Resistors
A bulb is a nonohmic resistor. Its voltage current graph does not follow a straight line. Instead, it gives a curve with an increasing slope. It shows that the resistance increases as the current increases.
Power
Power describes the at which electrical energy is transferred.
rate It is measured in Watts (W).
P
IV
P = Power (Watts) I = Current (Amps) V = Voltage (Volts)
P
IV
I
2
R
V
2
R
A light bulb has a resistance of 30Ω. What voltage would be required to run 4 Amperes of current through the bulb?
A.
120 V B.
7.5 V C.
.13 V D.
Voltron
A toaster is connected to a 120-Volt circuit and has 6 Amps of current running through it. What is the resistance of the toaster?
A.
720 Ω B.
20 Ω C.
.05 Ω D.
Depends on how brave he is.
If your body resistance is 100,000 Ω, how much current will you experience if you touch the terminals of a 12-Volt battery?
A.
1,200,000 A B.
8,333 A C.
.00012 A D.
Depends on how good it taste
How much power is dissipated in a toaster if it is connected to a 120 Volt circuit and uses 8 Amps?
A.
960 W B.
15 W C.
.067 W D.
Zero, it is powered by imagination
A light bulb has a power rating of 60-Watts. How much current would it pull if it has a resistance of 15 Ohms?
A.
4 A B.
2 A C.
900 A D.
30 A
The End!
Circuit Diagram
We draw electric circuits using specific symbols (because quite frankly most people can’t draw)….
cell resistor switch wires
Types of Circuits
There are two basic types of electrical circuits; SERIES CIRCUITS PARALLEL CIRCUITS
SERIES CIRCUITS
The components are connected end-to-end, one after the other. They make a simple loop for the current to flow round.
If one bulb ‘blows’ it breaks the whole circuit and all the bulbs go out. (One charge gets stuck, they all get stuck).
PARALLEL CIRCUITS
The components are connected side by side. The current has a choice of routes.
If one bulb ‘blows’ there will still be a complete circuit to the other bulb so it stays alight.
“Short Circuit”
Just remember that electricity is lazy , and will always take the path of least resistance .
If something (usually a wire) provides a path around a resistor, the electrons will take it!
COMPLEX CIRCUITS
Is made up of both series and parallel circuits combined.
This is what most circuits in the “real world” are like.
The End!
Resistances in Series
Resistors are said to be connected in when there is a single path series for the current.
I V T R 1 R 3 R 2 The current I each resistor is the same for R 1 , R 2 and R 3 .
The energy gained through
E
is lost through R 1 , R 2 and R 3 .
Only one current The same is true for voltages: For series connections: I = I 1 V T = V 1 = I 2 + V 2 = I 3 + V 3
Equivalent Resistance: Series
The sum equivalent resistance R e of a number of resistors connected in series is equal to the of the individual resistances.
I V T R 1 R 3 R 2 V T = V 1 + V 2 + V 3 ; (V = IR) I T R e = I 1 R 1 + I 2 R 2 + I 3 R 3 But . . . I T = I 1 = I 2 = I 3 Equivalent Resistance R e = R 1 + R 2 + R 3
Summary: Single Loop Circuits:
Resistance Rule: R e = S R
Current
:
I
S
E
S
R
Voltage Rule: S
E
= S IR R 2 R 1
E 1 E 2
Parallel Connections
Resistors are said to be connected in parallel when there is more than one path for current.
Parallel Connection: For Parallel Resistors: 2 W 4 W 6 W V 2 I 2 = V 4 = V 6 + I 4 + I 6 = V = I T T Series Connection: 2 W 4 W 6 W For Series Resistors: I 2 = I 4 = I 6 = I T V 2 + V 4 + V 6 = V T
Equivalent Resistance: Parallel
V T I T = V 1 = V 2 = I 1 + I 2 = V + I 3 3 Ohm’s law:
I
V R V T R e
V
1
R
1
V
2
R
2
V
3
R
3 V T Parallel Connection: R 1 R 2 R 3 1
R e
1
R
1 1
R
2 1
R
3 The equivalent resistance for Parallel resistors: 1
R e
i N
1
R i
1
Series and Parallel Combinations
In complex circuits resistors are often connected in both series and parallel . R 1 In such cases, it’s best to use rules for series and parallel resistances to reduce the circuit to a simple circuit containing one source of emf and one equivalent resistance.
V T V T R 2 R 3 R e
Example 4.
Find the equivalent resistance for the circuit drawn below (assume V T = 12 V).
V T 4 W 3 W 6 W
R
3,6 R e 3 W = 4 W W + 2 W R e = 6 W 4 W 12 V 2 W 12 V 6 W
Example 3 (Cont.) Find the total current I T .
R e = 6 W 4 W V T 3 W 6 W
I
V T R e
12 V 6 W I T = 2.00 A 4 W 12 V 2 W 12 V I T 6 W
Example 3 (Cont.) Find the currents and the voltages across each resistor .
4 W I 4 = I T = 2 A V T 3 W 6 W V 4 = (2 A)(4 W ) = 8 V The remainder of the voltage: (12 V – 8 V = 4 V ) drops across EACH of the parallel resistors.
V 3 = V 6 = 4 V This can also be found from V 3,6 = I 3,6 R 3,6 = (2 A)(2 W ) (Continued . . .)
V Example 3 (Cont.) Find the currents and voltages across each resistor .
4 = 8 V V 6 = V 3 = 4 V 4 W V T 3 W 6 W
I
3
V
3
R
3 4 V 3 W
I
6
V
6
R
6 4 V 6 W I 3 = 1.33 A I 6 = 0.667 A I 4 = 2 A Note that the junction rule is satisfied: S I (enter) = S I (leaving) I T = I 4 = I 3 + I 6
Kirchoff’s Laws for DC Circuits
Kirchoff’s first law: The sum of the currents entering a junction is equal to the sum of the currents leaving that junction.
Junction Rule: S I (enter) = S I (leaving) Kirchoff’s second law: The sum of the emf’s around any closed loop must equal the sum of the IR drops around that same loop.
Voltage Rule: S
E
= S IR