3-Current Electricity
3-Current Electricity
3-Current Electricity
1. Electric Current
2. Conventional Current
3. Drift Velocity of electrons and current
4. Current Density
5. Ohm’s Law
6. Resistance, Resistivity, Conductance &
Conductivity
7. Temperature dependence of resistance
8. Colour Codes for Carbon Resistors
9. Series and Parallel combination of
resistors
10. EMF and Potential Difference of a cell
11. Internal Resistance of a cell
12. Series and Parallel combination of cells
Electric Current:
SI unit- 1 Ampere
The electric current is defined as the charge flowing through any
section of the conductor in one second. 1 Ampere= 1 Coulomb/1 second
vd = - (eE / m) τ
Suppose a conductor of length l and area of cross section A and having elctrons density as n
A vd - - -E
Total No. of electrons in length l of conductor = nAl
I
Time required by the elctrons to cross the conductor from one end to another
T= l/vd
I= q/T I = neA vd
Current is directly proportional to drift velocity.
Current density at a point, within a conductor, is the current through a unit area of the conductor, around that point,
provided the area is perpendicular to the direction of flow of current at that point.
J = Vector Quantity
J = I / A = nevd
In vector form, I = J . A This shows that current I is a scalar product of 2
vector quanity i.e. Scalar Quantity
Ohm’s Law:
The electric current flowing through a conductor is directly proportional to the potential difference across the
two ends of the conductor when physical conditions such as temperature, mechanical strain, etc. remain the
same.
I
IαV or V α I or V = R I
I V
0 V
Resistance:
The resistance of conductor is the property by virtue of which the opposition is offered by the
conductor to the flow of electric current through it.
Resistance is directly
proportional to length and
R=V/I SI= ohm= V/A
inversely proportional to
cross-sectional area of the
Resistance in terms of physical features of the conductor: conductor and depends on
nature of material.
I = neA | vd |
L
R =ρ
I = neA (e |E| / m) τ A
ne2Aτ V
I= m
m L
where ρ =
ne2τ
V mL
= is resistivity or specific
I ne2Aτ resistance
m L
R =
ne2τ A SI = ohm metre
Resistivity depends upon nature of material and not on the geometrical dimensions of the conductor.
MOBILITY
It is defined as the drift velocity acquired by the charge carrier, when a unit Electric Field is applied across it.
𝞵= vd /E
I=neAE 𝞵
α=+ For most of the metals, the value of α is nearly 4 x 10-3 ℃-1
The resistivity of nichrome is weak Temp. dependence. At almost zero temp. Pure metal has negligibly
small resistivity but alloys still offer some resistivity due to their configuration.
Semi-Conductors and Insulators
We know,
ρ = 1/ n(T)
α=-
At room temperature (27.0°C), the resistance of a heating element is 100 Ω.
At what temperature does the resistance of the element change to 117 Ω?
Given that the temperature coefficient of the material of the resistor is 1.70
× 10–4 °C–1.
Ans- 1027 C
OHMIC and NON-OHMIC Device
Ans- 6 x 10-13 A
Eg.A battery of emf 2V and internal resistance 0.5 Ohm is connected across a
resistance of 9.5 Ohm. How many electrons cross through a cross section of the
resistance in 1 second?
Internal Resistance of a cell:
The opposition offered by the electrolyte of the cell to the flow of electric current through it is called
the internal resistance of the cell.
Work done in carrying Work done in carrying a unit Work done in carrying a unit A E r B
a unit charge along the = charge from A to B against + charge from B to A against the
v
complete circuit the external resistance R internal resistance r I I
R
Eq0 = Vq0 + vq0
V
V- Potential drop across the
E =V+v resistance of the external circuit
= V + Ir
Ir = E - V v- Potential drop across the
resistance offered by Electrolyte
Dividing by IR = V,
Ir E–V E
= r =( - 1) R
IR V V
Characteristic curves of a CELL
E vs R graph
The emf of a cell is the potential difference when no current is drawn from the circuit
Thus, emf is independent of the Resistance of the circuit
V vs R Graph V vs I Graph
E =V+v
V=E-v
As R increases, R=0 V=0
V=E-Ir
V also Increases R=r V=E/2
R= ∞ V=E V=-Ir+E
Y=mx+c
Eg.A battery of emf 2V and internal resistance 0.5 Ohm is connected across a
resistance of 9.5 Ohm. How many electrons cross through a cross section of the
resistance in 1 second?
If we wish to replace these 2 cells with one cell of Equivalent Emf, then
I= (E1-V)/r1 + (E2-V)/r2
mR + nr = 0
R = nr/m
Or Rm=nr
Find the net resistance of the circuit shown.
Ans= 1/3 A]
ELECTRIC POWER
The rate at which work is done by a source of emf in maintaining an electric current through a circuit.
1hp=746W
ELECTRIC ENERGY
The total work done by the source of emf in maintaining an Electric current in a circuit for a given time
ELECTRIC EFFIECIENCY
The efficiency of an electric device is defined as the ratio of output power to the input power
POWER RATING
It is the electrical energy consucmed by the appliance per second.
CURRENT ELECTRICITY - II
I1 I2
The algebraic sum of electric currents at a junction in any electrical
network is always zero. I3
O
I5
I1 - I2 - I3 + I4 - I5 = 0
I4
Sign Conventions:
1. The incoming currents towards the junction are taken positive.
2. The outgoing currents away from the junction are taken negative.
Note: The charges cannot accumulate at a junction. The number of charges that arrive at a junction
in a given time must leave in the same time in accordance with conservation of charges.
II Law or Voltage Law or Loop Rule:
The algebraic sum of all the potential drops and emf’s along any closed
path in an electrical network is always zero.
I1 E1 I1
R1
A B Loop ABCA:
3. The potential fall is taken negative. Note: The path can be traversed in clockwise
4. The potential rise is taken positive. or anticlockwise direction of the loop.
Wheatstone Bridge: B
G
When the galvanometer current is made
zero by adjusting the jockey position on A B
the metre-bridge wire for the given values
l cm J 100 - l cm
of known and unknown resistances,
K
E
R RAJ R AJ R l
Therefore, X = R (100 – l) ⁄ l