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ELECTRIC CURRENT AND DIRECT CURRENT CIRCUIT (Electrical measurement…
ELECTRIC CURRENT AND
DIRECT CURRENT CIRCUIT
Electrical Conduction
Electric current, I
Direction of electric field or electric current:
Positive to negative terminal
Direction of electron flows:
Negative to positive terminal
Electric current, I is defined as the total (net) charge, Q flowing through the area per unit time, t.
Q= It
unit : ampere(A)
Current Density,J
Is defined as the current flowing through a conductor per unit cross-sectional area.
J = I/A
unit : A m-2
Electrical coduction in metal
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
Consider a metal rod of length L and cross-sectional area A, which is applied to the electric field
Vd = I / nAe
or
Vd = J / ne
Electromotive Force (emf), Internal
Resistance and Potential Difference
Emf, ε and potential difference, V
emf
defined as the energy provided by the source (battery/cell) to each unit charge that flows through the external and internal resistances.
potential difference
the work done in bringing a unit (test) charge from the negative to the positive terminals of the battery through the external resistance only.
When the current I flow naturally from the battery there is an internal drop in potential difference (voltage) equal to Ir. Thus, the terminal potential difference (voltage), V is given b
V=ε−Ir
Equation V = ε – Ir is valid if the battery (cell) supplied the current to the circuit where V < ε
For the battery without internal resistance or if no current flows in the circuit (open circuit), then equation V = ε – Ir can be written as V=ε
Internal resistance,r
Is defined as the resistance of the chemicals inside the battery (cell) between the poles and is
given by
Kirchhoff’s Laws
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.
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.
For e.m.f
For IR
Electrical measurement devices
Volmeter
-A device that measures voltage.
-Are connected in parallel or across the element whose voltage they are measuring
Ohmmeter
Used to 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.
Ammeter
-Measures current.
-Connected in series with the element whose current they are measuring.
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 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)
Multiplier
-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)
Resistivity and Ohm’s Law
Resistance,R
Is that property which opposes or limits current in an electrical circuit.
R = V / I
unit = VA-1
Resistance depends on :
Type of material it is made
Length
Cross-sectional area (A)
Temperature
Resistivity,ρ
defined as the resistance of a unit cross-sectional area per unit length of the material.
ρ = RA / l
unit = ohm meter ( m)
Conductivity,σ
Is defined as the reciprocal of the resistivity of a material.
σ = 1 / ρ
unit = ohm− 1m− 1.
Ohm's Law
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 = IR
unit : Voltage(V)
Combinations of Resistors
Series
V=V1+V2+V3
RE=R1+R2+R3
I1=I2=I3
Parallel
V1=V2=V3
1/RE=1/R1+1/R2+1/R3
I=I1+I2+I3
Electrical Energy and Power
Electrical energy,E
Consider a circuit consisting of a battery that is connected by wires to an electrical device (such as a lamp, motor or battery being charged)
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 ;
Q= It
Then the work done on this charge Q from B to A (equal to the electrical energy supplied) is ;
W =QV
Power,P.
Is defined as the energy liberated per unit time in the electrical device.
P = IV
unit : Watt(W)
