Current electricity notes

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UNIT-II
CHAPTER-3 : CURRENT ELECTRICITY
1. ELECTRIC CURRENT (I) :
The rate of flow of electric charge across any cross-section is called electric current.
dq
(a) Instantaneous electric current I 
dt
q
(b) Average electric current Iav 
t
2. CURRENT DENSITY (J) :
Current flowing per unit area through any cross-section is called current density.




®
I A I
J  I  J.A  JAcos 
A

3. DRIFT VELOCITY (Vd) :
Average velocity with which electrons drift from low potential end to high potential end of the
e
conductor (vd). Drift velocity is given by vd   E (in terms of applied electric field)
m
I
vd  (in terms of current through the conductor)
neA

I  neAvd where A is the area of cross-section and “Avd” represents the rate of flow.

vd v e
Mobility : The term is called mobility of charge carriers, represented by   d  .
E E m
SI unit of mobility = m2/Vs
4. OHM’S LAW :
V 1  1
I where R   where  (resistivity) =
R A A (conductivity)
Hence according to Ohm’s law when R is constant I V  I – V curve is a straight line
(at constant temperature).
 Resistance of a conductor is given by
 m
R  2
A ne A
where  is resistivity. Its unit is -m.
m
 Resistivity of a conductor,   (where m is mass of electron, n is number density of free
ne 2 
electrons,  is average relaxation time).
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5. TEMPERATURE DEPENDENCE OF RESISTANCE AND RESISTIVITY :
(i) For conductor
For conductor, resistance and resistivity increases with increase in the temperature.
  t = 0(1+t), where ‘’ is temperature coefficient of resistivity.
As R   R = R0(1 + t)

(R0 is the resistance at reference temperature)
At temperature t1, R1 = R0 (1 + t1)
At temperature t2, R2 = R0 (1 + t2)
R 2  R1
     
R 0 (t 2  t1 )
O For nichrome wire T




(ii) For Semiconductor
 ®
Resistivity T of copper as a function of temperature T




T
Temperature dependence of resistivity for a typical semiconductor.
For Semiconductors resistance and resistivity decreases with increase in the temperature.
(iii) For Alloy
Alloys (like nicrome and manganin etc) exhibit a very weak dependence of resistivity with
temperature.
6. ELECTRIC ENERGY & ELECTRIC POWER :
Electric Energy :
For a charge q, accelerated with potential V, the electric energy is expressed as qV or Vit.
When a current is passed through a resistor energy is consumed in over coming the resistance of
the wire. This energy is converted into heat (Heating effect of electric current).
2 V2
W = VIt = I Rt = t
R
SI unit = joule (J)
Commercial unit of electrical energy consumption :
1 unit of electrical energy
= kilowatt hour
= 1 kWh = 3.6 × 106 joule or J
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Electric power :
Power consumed by a resistor
V2
P = I2R = VI =
R
SI unit = watt (W)
7. CELL :
• EMF (E):The potential difference across the terminals of a cell when no current is drawn from it.
• Internal Resistance (r) : It is the opposition offered by the electrolyte to the flow of current
through it.
It depends on :
(i) Distance between electrodes.
(ii) Surface area of electrodes in contact with electrolyte.
(iii) Temperature.




®
Series grouping
E1 r E2 r E3 r n cells
+ – 1
+ – 2 + – 3



i


R
(a) Eequivalent = E1 + E2 + E3 + ....... En
(b) requivalent = r1 + r2 + r3 + ...... rn

(c) Current i  E i

r R
i


nE
(d) If all cells have equal emf E and equal internal resistance r then i 
nr  R
Cases : E1 r1
E nE
(i) If nr >> R  i  (ii) If nr << R  i  E 2 r2
r R
Parallel Grouping E 3 r3
E1 E 2 E 3
   ......
r1 r2 r3
(a) E equivalent 
1 1 1 n cell
   ........ i
r1 r2 r3
1
(b) requivalent 
1 1 1
   ......
r1 r2 r3 R
(c) If all cells have equal emf. E and internal resistance r then E equivalent = E
r E
requivalent   current i  r
n n R


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