ELECTRIC CURRENT & DIRECT CURRENT CIRCUIT (3.2 RESISTIVITY AND OHM'…
ELECTRIC CURRENT & DIRECT CURRENT CIRCUIT
3.1 ELECTRICAL CONDUCTION
Electric Current (I)
Electric current, I is defined as the total (net) charge, Q flowing through the area per unit time, t. S.I unit = Ampere (A)
I = Q/t
Current Density (J)
Is defined as the current flowing through a conductor per unit cross-sectional area.Its unit is ampere per square meter (A m-2). The direction of current density, J always in the same direction of the current I.
J = I/A
Electrical Conduction in Metal
In metal the charge carrier is free electrons and a lot of free electrons are available in it.
When the electric field is applied to the metal, the freely moving electron experience an electric
force and tend to drift with constant average velocity called drift velocity towards a direction
opposite to the direction of the field.
Drift Velocity in Charges, Vd
Vd = I/nAe
Vd = J/ne
n = free electrons per unit volume
A = cross-sectional area
e = charge of electrons
3.2 RESISTIVITY AND OHM'S LAW
Property which opposes or limits current in an electrical circuit. S.I unit is Ohm.
R = V/I
Resistance of a conductor depends on:
Type of material
Is defined as the resistance of a unit cross-sectional area per unit length of the material.It is a measure of a material’s ability to oppose the flow of an electric current. Its unit is ohm meter. A good electric conductor have a very low resistivity and good insulators have very high
ρ = RA/L
Is defined as the reciprocal of the resistivity of a material. Its unit is one per ohm meter.
σ = 1/ρ
States that the voltage drop across a conductor, V is proportional to the current, I through
it if its physical conditions & temperature are constant.
V is directly proportional to I.
V = IR
3.3 EMF, INTERNAL RESISTANCE AND POTENTIAL DIFFERENCE
For the current to flow continuously from terminal A to B, a source of electromotive force
(e.m.f.), ε is required such as battery to maintain the potential difference between point A and
Electromotive force (emf), ε is defined as the energy provided by the source (battery/cell) to
each unit charge that flows through the external and internal resistances.
Terminal potential difference, V is defined as the work done in bringing a unit charge from the negative to the positive terminals of the battery through the external resistance
only.The unit for both e.m.f. and potential difference are volt (V).
V = ε - Ir
For the battery without internal resistance or if no current flows in the circuit (open circuit),
then V = ε.
Internal resistance (r)
Defined as the resistance of the chemicals inside the battery (cell) between the poles and is
Vr is voltage across internal resistance.
3.4 ELECTRICAL ENERGY & POWER
Eletrical Energy (E)
Its unit is Joule (J)
W = QV
W = E = VIt
Is defined as the energy liberated per unit time in the electrical device.
P = W/t = VIt/t
P = IV
When the electric current flows through wire or passive resistor, hence the potential difference
across it is V = Ir then the electrical power can be written as below. Its unit is Watts (W).
P = I^2 R
P = V^2/R
3.5 COMBINATION OF RESISTORS
Current : I = I1 = I2 = I3
Volatge : V = V1 + V2 + V3
Equivalent Resistance : R = R1 + R2 + R3
Current : I = I1 + I2 + I3
Voltage : V = V1 = V2 = V3
Equivalent Resistance : 1/R = 1/R1 + 1/R2 + 1/R3
3.6 KIRCHOFF'S LAWS
Kirchoff's First Law
States the algebraic sum of the currents entering any junctions in a circuit must equal the
algebraic sum of the currents leaving that junction.
I (in) = I (out)
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
Solving the simultaneous equation to determine the unknown currents and unknown
Kirchoff's Second Law
States in any closed loop, the algebraic sum of emfs is equal to the algebraic sum of the
products of current and resistance.
Sum of ε = Sum of IR
3.7 ELECTRICAL MEASUREMENTS DEVICE
Device that measures current
Connected in series with the element whose current
they are measuring.
Have zero resistance so
that the current being measured is not altered.
A device that measures voltage.
Are connected in parallel or across the element
whose voltage they are measuring.
Has infinite resistance so that no
current passes through it.
Used to measure the resistance.
Consists of a meter, a resistor & a source connected
The resistance R to be measured is connected
between terminals X & Y.
Is a current- sensitive device whose needle
deflection is proportional to the current through its
Operates on magnetic principles
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)
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)