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Electric Current and Direct Current Circuit (Electrical Conduction…
Electric Current and Direct Current Circuit
Electrical Conduction
Electric current, I
The total (net) charge, Q flowing through the area per unit time, t
Current density, J
The current flowing through a conductor per unit cross-sectional area
Electrical conduction in metal
In metal the charge carrier is free electrons and a lot of free electrons are available in it
They move freely and randomly throughout the crystal lattice structure of the metal but frequently interact with the lattices
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 of charges, Vd
Kirchhoff’s Laws
Kirchhoff’s first law (junction or current law)
The algebraic sum of the currents entering any junctions in a circuit must equal the algebraic sum of the currents leaving that junction
Kirchhoff’s second law (loop or voltage law)
In any closed loop, the algebraic sum of emfs is equal to the algebraic sum of the products of current and resistance
Electromotive Force (emf), Internal Resistance and Potential Difference
Emf, ε and potential difference, V
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 (voltage), V is defined as the work done in bringing a unit (test) charge from the negative to the positive terminals of the battery through the external resistance only
Internal resistance of a battery, r
The resistance of the chemicals inside the battery (cell) between the poles and is given by
Electrical Measurement Devices
Ammeter
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
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
Ohmmeter
measure the resistance
Consists of a meter, a resistor & a source connected in series
The resistance R to be measured is connected between terminals X & Y
Galvanometer
Is a current- sensitive device whose needle deflection is proportional to the current through its coil
Operates on magnetic principles
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)
Combination of Resistors
Series Circuit
Parallel Circuit
Resistivity and Ohm's Law
Resistance (R)
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
Resistance of a conductor depends on
Type of material it is made
Its length (L)
Its cross-sectional area (A)
Its temperature (T)
Resistivity, ρ
The resistance of a unit cross-sectional area per unit length of the material
A measure of a material’s ability to oppose the flow of an electric current
Conductivity, σ
The reciprocal of the resistivity of a material
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
Electrical Energy and Power
Electrical energy, E
A current I flow from the terminal A to the terminal B, if it flows for time t, the charge Q which it carries from B to A is given by
Then the work done on this charge Q from B to A (equal to the electrical energy supplied) is
Power, P
The energy liberated per unit time in the electrical device
The electrical power P supplied to the electrical device is given by
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
For emf, ε
For product of IR
Direction of electric field or electric current
Positive to negative terminal
Direction of electron flows
Negative to positive terminal
unit is ohm meter
scalar quantity
S.I. unit of the electric current is the ampere (A)
scalar quantities
vector quantity
unit is ampere per square meter (A m-2)
The direction of current density, J always in the same direction of the current
SI unit: Ohm (Ω) @ V A-1
Good electric conductor have a very low resistivity and good insulators have very high resistivity
The resistance of a conductor depends on the length and cross-sectional area
scalar quantity
unit for both e.m.f. and potential difference are volt (V)
scalar quantity
unit is watts (W)
