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ELECTRIC CURRENT AND DIRECT CURRENT CIRCUIT (Electrical Measurement…
ELECTRIC CURRENT AND DIRECT CURRENT CIRCUIT
Resistivity and Ohm's Law
Resistance
Property which opposes or limits current in an electrical circuit
The ratio of the applied voltage (PD) to the current that flows through the conductor.
R = V/I
If R is constant, V I
SI unit = Ohm () @ VA^-1
Resistance of a conductor depends on
Type of material it is made
Its length (L)
Its cross-sectional area (A)
Its temperature (T)
constant temperature,
R L/A
R = ρL/A
Where ρ is the proportionality constant
called resistivity.
Resistivity,ρ
ρ = RA/L
Where l is length of material,
A is cross-sectional area
the resistance of a unit cross-sectional area per unit length of the material.
It is a scalar quantity and its unit is ohm meter ( m)
It also known as specific resistance.
Resistivity depends on the type of the material and on the temperature.
A good electric conductor have a very low resistivity and good insulators have very high
resistivity
Conductivity,σ
the reciprocal of the resistivity of a material.
σ = 1/ρ
Scalar quantity
its unit is −1 m−1.
Ohm's law
the voltage drop across a conductor, V is proportional to the current, I through it if its physical conditions & temperature are constant.
V. I
V = IR
V= voltage across
I = current flow through
R = resistance
can be express in terms of J & E
V = IR
V =EL , I = JA , R = ρL/A
EL = (JA)ρL/A
E = ρJ
ρ = 1/σ , J = σE
Materials that obey J = σ E are said to follow Ohm’s Law & this type of materials are known as
Ohmic material.
Combination of Resistors
Electrical Conduction
Electric current,I
The total (net) charge,Q flowing through the area per unit time,t.
I = Q/t = dQ/dt
Scalar quantity
Unit = ampere (A)
1 ampere = 1 coulomb/1 second = 1 Cs^-1
Positive terminal to negative terminal
(direction of electric field or electric current)
Negative terminal to positive terminal
(direction of electron flows)
Current density,J
The current flowing through a conductor per unit cross-sectional area.
J = I/A
I = electric current
A = sectional area of conductor
Unit = Am^-2
Vector quantity
Direction current density always in the same direction of the current,I.
Electrical conduction in metal
The charge carrier in metal is free electrons.
They move freely and randomly throughout the crystal latticr structure of the metal but frequently interact with the lattices.
When the elctric field is applied to the metal,the freely moving electron experience an electric force and tend to drift with constant average velocity (drift velocity) towards a direction opposite to the direction of the field.
The magnitude of the drift velocity is much smaller than the random velocities of the free electron.
Drift velocity of charges,Vd
there are n free electrons (charge carrier) per unit volume in the metal rod,
n =N/V
V = AL
n = N/AL
N = nAL
Total charge of free electron
Q = Ne
Q = (nAL)e
Vd = L/t
Vd = I/nAe
J = I/A , Vd = J /ne
Kirchhoff's Law
Kirchhoff's first law (junction or current law)
States that the algebraic sum of the currents entering any junctions in a circuit must equal the algebraic sum of the currents leaving that junctions.
Σ IIN = Σ IOUT
Kirchhoff's second law (loop or voltage law)
States that in any closed loop,the algebraic sum of emfs is equal to the algebraic sum of the products of current and resistance.
Σ ℰ = Σ IR
Problem solving strategy
Choose and labelling the current at each junction in the circuit given.
Choose any one junction in the circuit and apply the Kirchhoff's first law.
Choose any two closed loops in the circuit and designate a direction (clockwise or anticlockwise) to travel around the loop in applying the Kirchhoff's second law.
Solving the stimultaneous equation to determine the unknown currents and unknown variables.
Electrical Measurement Devices
Ammeter
A device that measures current.
Connected in series with the element whose current they are measuring.
Ideally, an ammeter should have zero resistance so
that the current being measured is not altered.
Voltmeter
A device that measures voltage.
Connected in parallel or across the element whose voltage they are measuring.
An ideal voltmeter has infinite resistance so that no
current passes through it.
Galvanometer
A current-sensitive device whose needle deflection is proportional to the current through its coil.
Operates on magnetic principles
Ohmmeter
A device that measures resistance.
Consists of a meter, a resistor & a source connected
in series.
The resistance R to be measured is connected
between terminals X & Y.
To use the Ohmmeter:
1st connect X directly to Y & adjust Rs until meter
reads zero.
Then connect X & Y across the resistor R to be
measured & read the scale.
Shunt
Galvanometer can be converted to a useful ammeter by placing a shunt resistor Rs in parallel with the galvanometer.
Value of Rs must be less than the
galvanometer resistance. (Rs << r)
Multiplier
Galvanometer can be used as a voltmeter by adding a multiplier resistor RM in series with it.
RM must have a value much greater than the
resistance of the galvanometer. (RM >> r)
Electromotive Force (emf),Internal Resistance and Potential Difference
Emf,ℰ and potential difference,V
Electromotive force,
The energy provided by the source (battery/cell) to each unit charge that flows through the external and internal resistances.
Terminal potential difference(voltage),V
The work done in bringing a unit charge from the negative to the positive terminals of the battery through the external resistance only.
V = ℰ - Ir. V < ℰ
V = IR.
V = terminal potential difference
Ir = internal drop in potential difference,Vr
R = total external resistance
r = internal resistance of a cell (battery)
For the battery without internal resistance or if no currrent flows in the circuit (open circuit),
V = ℰ - Ir. (V = ℰ)
Unit for emf and potential difference = Volt (V)
Internal resistance of a battery,r
The resistance of a chemicals inside the battery (cell) between the poles.
Vr/I
Vr = potential difference across internal resistance
I = current in the circuit
Electrical Energy and Power
Electrical energy,E
The charge,
Q = It
Work done on this charge,
W = QV
W = E = VIt (Joule,J)
Power,P
The energy liberated per unit time in the electrical device.
Electrical power,P supplied to the electrical device,
P = W/t
= VIt/t
P = IV
Electric current flows through wire or passive resistor,
Potential difference,
V = Ir
Electrical power,P
P = I^2R
P = V^2/R. (Watt,W)
Scalar quantity
