bt401p

ELECTRIC CURRENT A flow of charge from one place to another. The unit is Ampere , which equal to a flow of 1 coulomb per second.

Moving charges as a current
Its described as a stream of moving charges.
May range very small currents such as the nerve impulses to a large as the solar wind emitted by the sun.
There must be a “net” flow of charges towards one direction.

When moving charges is not a current
When there is no net flow of charge even though there are actual movement.
Example:
Electrons of a copper conductor in absence of electric potential.
Electrons just move randomly the charge flowing charge flowing to one direction is equal to those flowing to the other direction.

Electric current in a conductor
An isolated conductor in absence of electric potential contains free flowing electrons but no electric current.
Isolated conductor charges

continuation:
A conductor connected to a dry cell or battery has the necessary electric potential to influence the flow of charges towards one direction, hence producing current.
Battery + - Conductor Charges Direction of charges

continuation:
Electric current ( I ) is defined as the amount of charges passing through a hypothetical plane intersecting the conductor per unit of time.
Its unit is coulomb per second (C/s), also called ampere (A).
Where:
I = Current (ampere, A)
Q = Charge (coulomb, c)
t = Time (second, s)

continuation: - - - - - - t = t 0 t = t 0 + 1 s plane plane

continuation:
Independent to the selection of hypothetical plane
a b c a’ b’ c’ I I

Sample problem:
A wire carries a current of 0.8 ampere. How many electrons passes every section of the wire every one second?

Current is a scalar quantity
Electric current is moving along a conductor has only two possible directions.
Electric current are scalars. Adding and Subtracting the current does not consider the orientation of the conductor in space.

continuation: I 0 I 1 I 2 I 0 = I 1 + I 2

DIRECTION OF CURRENT
In reality, electric current are movement of electrons along the conductor.
For historical reason, current is treated as flow of positive charges to the direction opposite that of the actual movement of electrons.

continuation:
These positive charges are not actual particles. They are called holes , vacant spaces where there should be an electron. The charge of a hole is +1.6 x 10 -19 C .
Electrons are known as negative charge carriers . Holes are known as positive charge carriers .

Drift Speed
The net motion of charged particles as a group:
Where: I = electric current (A) n = charge concentration v d = drift velocity (m/s) e = charge of electron A = cross-sectional area of conductor(m 2 )
Usually very small (10 -5 or 10 -4 m/s) compared to random motion of charges (10 6 m/s)
I in I in A

Current Density
Current per unit of cross-sectional area of a conductor.
A vector quantity with the same direction as the motion of positive charge carriers.
Where: I = electric current (A) J = current density (A/m 2 ) n = charge concentration v d = drift velocity (m/s) e = charge of electron A = cross-sectional area of conductor(m 2 )

Sample Problem:
A 491 gauge copper wire has a nominal diameter of 0.64 mm. This wire carries a constant current of 1.67 A to a 4,910 watts lamp. The density of free electron is 8.5 x 10 28 electrons/m 3 . Find the current density and the magnitude of drift velocity.

Types of Current
Direct current
The direction of current is constant.
The graph of current vs time is a straight line.
Developed by Tomas Alva Edison
Soon replaced by alternating current as primary means of transmitting electricity, but still used in battery operated devices.

continuation:
Alternating Current
The direction and magnitude of the current continuously changes between two extremes.
The graph of current vs time is sinosoid.
Developed by Nikola Tesla and George Westinghouse , forming rivalry with Thomas Edison on War of the Currents .
The most commonly used method of electric transmission today.

Types of Current
Direct Current
Alternating Current I (A) t (s) I (A) t (s)

ELECTRIC RESISTANCE

Electric Resistance
Property of the conducting medium that weakens the transmission of electric current.
Denoted as R and its unit is Ohm ( Ω ) .
Where: R = Resistance (Ohm, Ω ) ρ = resistivity ( Ω m) L = Length of the wire (m) A = cross-sectional area of a wire(m 2 )

Sample Problem:
A piece of 1.0 m wire has a resistance of 0.19 ohms. Calculate the resistivity of the wire. The cross-sectional area of the wire is 0.5 mm 2 .
ρ L A

Resistivity & Conductivity
Resistivity ( ρ )
Measure of how much resistance a material possesses against electric current.
Intrinsic property of a material that depends on its electronic structure.
Conducting material Electric field

continuation:
Measure by placing the material between two plates with constant electric field ( E ) and taking the ratio of electric field and current density ( J ) .
Varies with temperature
Where: ρ = resistivity ( Ω m) E = electric field (N/c) J = current density (A/m 2 )

Conductivity
Measure of how the material is capable of conducting electricity.
Reciprocal of resistivity.
continuation:

Variation of Resistivity with Temperature
Over a wide range of temperature, the graph of resistivity vs temperature of metal is linear.
400 200 0 1200 1400 2 8 0 4 6 10 600 800 1000 Resistivity 10 -8 Ω m Room temperature Temperature (Kelvin)

Variation of Resistivity with Temperature
Thus it can be represented by a Linear equation.
Where: ρ = resistivity ( Ω m) ρ 0 = resistivity at room temperature ( Ω m) T = temperature (Kelvin,K) T 0 = room temperature (K) α = coefficient of resistivity (K -1 )

continuation:
The Temperature coefficient of resistivity ( α ) determines how much resistivity increases with temperature.
Its unit is (per Kelvin)K -1 .

Sample Problem:
What is the resistivity of iron at 200K? Use the values of resistivity (at room temperature) and temperature coefficient of the resistivity in the handout.

Ohm’s Law
The current I (Ampere, A) is directly proportional to the potential difference V (Volt,V) with resistance R (ohms, Ω ) as the proportionality constant.

continuation:
Assumed that the resistance does not vary with voltage or current.
Not all conducting material follow “Ohm’s Law”. Those are follow are said to be ohmic , while those that do not are said to be non ohmic .

Current Potential Difference graph of a 1000 W resistor , an Ohmic device. -4 -2 0 +2 +4 -2 +2 0 Current (mA) Potential Difference (V)

Current vs Potential Difference graph of a pn junction diode , a non-ohmic device. -4 -2 0 +2 +4 -2 +2 0 Current (mA) Potential Difference (V)

Single Loop Circuit
Circuit
Close network of electronic devices through which current constantly flows.
EMF Device Maintain potential difference. Provides steady flow of charge. EMF stand for Electromotive force . R EMF I + - + - I

The Resistor
Provides a resistance to the circuit.
It was specially designed to only provide certain amount of resistance.
An Ohmic device
Such conductor device.
It was verified experimentally by the German physicist Georg Ohm (1787-1854).

Electromotive Force
A circuit consists of electrons from the negative terminal of a battery to the positive terminal of the battery.
Electrons must then return to the negative terminal, or current will stop flowing.
The electron are forced into this higher potential by a electromotive force.
EMF

continuation:
EMF Devices:
Battery or Dry Cell
Electrochemical Cell
Electric Generator
Photovoltaic Cell

Internal Resistance
The resistance found inside real batteries
Lessen the output voltage of the battery.
Denoted as r i
Its SI unit is Ohms (Ω) .
A real battery is now drawn as:
continuation: EMF r i

continuation:
Terminal Potential Difference ( TPD )
The output voltage of a source of emf after internal resistance takes effect.
The equation used to solve for terminal potential difference is:
TPD = E – Ir i
Where:
TPD = voltage across the source (V)
E = voltage if the source is ideal emf (V)
r i = internal resistance of the source (Ω)
I = current flowing through the battery (A)

Sample Problem:
A 6.0 V battery is connected to an external 6.0 0hms resistor.
What is the value of the current flowing through the external circuit if there is no internal resistance,
What is the value of the current flowing through the external circuit when the internal resistance is 0.3 ohms?

Resistors in Single Loop Circuit

Where: R is resistance, I is electric current and V is electric potential difference.
Resistors in Series Circuit. R 3 V T I T + - + R 2 + R 1 + - - - R T

Equivalent resistance in a Series Circuit

Sample problem:
Resistors R 1 = 2.00 ohms, R 2 = 3.00 ohms and R 3 = 4.00 ohms are in series connection with a voltage source of 100.0 volts. Find the equivalent resistance, electric current and electric potential difference.

Resistor in Parallel Circuit
R 3 V T I T + - + R 2 + R 1 + - - - R T I 3 I 2 I 1

Equivalent resistance in a Parallel Circuit

Sample problem:
Resistors R 1 = 3.00 ohms, R 2 = 5.00 ohms and R 3 = 7.00 ohms are in parallel connection with a voltage source of 110.0 volts. Find the equivalent resistance, electric current and electric potential difference.

Resistors in Single Loop Circuit
Resistor in Series-Parallel Circuit
R 3 V T I T + - + R 2 + R 1 + - - - R T

POWER IN CIRCUITS

The Power in the Circuits
Flow of current across a circuit.

continuation:
Movement of a charge across a electric device:
It moves from higher potential to lower potential.
Hence, there is a decrease in potential energy.
Q

continuation:
If there is a decrease in potential energy, there must be a transmission to another form of energy.
Light bulb: to heat and light.
Electric motor: to mechanical energy
Resistor: Internal energy/heat.

continuation:
The rate at which electric potential energy is transformed to another form of energy is the POWER in the circuit.

Sample Problem:
A current flowing through a 25.0 ohm resistor is 2.0 A. How much power is dissipated by the resistor.

MULTILOOP CIRCUIT
Provides multiple paths for current.
When one component was cut-off, others can still function.

What happen when one component in a series circuit was cut-off?

What happen when one component in a multiloop circuit was cut-off?

continuation:
Current in a Multiloop Circuit
The point where three or more segments of the conductor meet is called the junction.
The current split at the junction.
Junction current

GUSTAV KIRCHHOFF
German physicist who, in the collaboration with Robert William Bunsen, develop ed the science of spectrum analysis.
He showed that each element, when heated to incandescence.
He produced a characteristic pattern of emission lines.
He formulated Kirchhoff’s Law for electric circuit.
(1824-1887)

In any closed circuit, the algebraic sum of all EMF’s and potential drop is equal to zero. (Using loop direction)
KIRCHHOFF’S LAW R 2 + Emf 1 + - R 1 + Emf 2 + - R 3 + Loop 1 Loop 2 I 1 I 2 I 3 -

At any point in a circuit, the sum of the currents leaving the junction point is equal to the sum of all the current entering the junction point. (Using current direction).
KIRCHHOFF’S LAW R 2 + ε 1 + - R 1 + ε 2 + - R 3 Junction point I 1 I 3 I 2 +

Sample Problem:
In a given circuit below, Find: a) I 1 , b) I 2 and c) I 3
10 Ω + 9v + - 15 Ω + 12v + - 5 Ω I 1 I 3 I 2 +

RC CIRCUIT (Resistor and Capacitor in a circuit)

Resistor- Capacitor in a circuit.
R + - C S 1 S 2 ε + - Where: ε = Batteries (Emf) S 1 & S 2 = Switches R = Resistor C = Capacitor Open Close

Charging a capacitor R + - C S 1 S 2 ε + - I I I I I closed open Where: V R = Potential difference across the resistor. V C = Potential difference across the capacitor. I

continuation
Current I O at the moment S 1 closed ( t = 0)
Current I at any time t after S 1 closed:
After some time t
The charge of the capacitor (q) increases
Current ( I ) decreases.

continuation
Until the capacitor reaches its equilibrium charge (q eq ), happen when V C reaches V C = ε , which result to I = 0

continuation
Charge and current of the capacitor at any given time t after t = 0.

The time constant ( τ ) of RC series circuit.
The unit of time constant is second.
At time t = τ
Q = 0.63 C ε
I = 0.37 I o
The charging time of RC circuits are often stated in terms of time constant.
continuation

Sample Problem:
A resistor with resistance R=1.0 x 10 6 Ω , capacitor with capacitance C=2.2 x 10 -6 F, a voltage source with ε = 100 v, and a switch are all connected in a single loop series circuit. The switch is initially open. When the switch is closed, calculate:
Initial current across the resistor
Equilibrium charge of the capacitor
Time constant of the circuit
Current through the resistor after 5 seconds
Charge of the capacitor after 5 second
Charge of the capacitor at t = τ

bt401p

by jeric lora on Jan 07, 2010

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