03 Electricity
3
Direct Current and Electric Current 1. Electric current: An electric current i in a conductor is defined by dq i dt = . By convention, the direction of electric current is taken as the direction in which positive charge carriers would move. 2. Current density: Current density is related to the current as i J dA = ⋅ , where dA is a vector perpendicular to a surface element of area dA, and the integral is taken over any surface cutting across the conductor. J has the same direction as the velocity of the moving positive charges. 3. Drift speed: When an electric field E is established in a conductor, the charge carriers (assumed positive) acquire a drift speed v d in the direction of E ; the velocity is related to current density J as : d J (ne)v = . 4. Resistance of a conductor: If V is the p.d. applied across the conductor and i is the corresponding current, then its resistance is defined as: R = V/i. 5. Change in ρ or R with temperature: If R 0 is the resistance of a wire at temperature 0°C, then resistance at any temperature t is t 0 R R (1 t) +α , where α is the temperature coefficient of resistance. It can be defined as t 0 dR 1 R dt α= . 6. Ohm’s law: Under given physical conditions the current i produced in the conductor is proportional to the applied potential difference across the conductor. 7. Combination of cells: i) In series: If n identical cells each of emf ξ and internal resistance r are connected in series, then current in external resistor R: n i nr R ξ = + , in case when nr << R, i n R ξ . ii) In parallel: i r R n ξ = + , in case R << nr, i n r ξ . iii)Series-parallel: If n cells are connected in series and m cells are in parallel, then n i nr R m ξ = + . 8. Delta-star transformation: A combination of three resistors in the form of delta can be effectively converted into star. A delta of three resistors R 1 ,R 2 and R 3 in equivalent to a star with three resistors R 12 ,R 13 and R 23 , where 1 2 12 1 2 3 1 3 13 1 2 3 2 3 23 1 2 3 RR R R R R RR R R R R RR R R R R = + + = + + = + + Delta of three resistors A B C R 1 R 3 R 2 A B C R 12 R 13 R 23 Star of three resistors
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Electricity for iitjee
Transcript of 03 Electricity
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Direct Current and Electric Current
1. Electric current: An electric current i in a conductor is defined by dqidt
= .
By convention, the direction of electric current is taken as the direction in which positive charge carrierswould move.
2. Current density: Current density is related to the current as i J dA=
, where dA
is a vectorperpendicular to a surface element of area dA, and the integral is taken over any surface cutting acrossthe conductor. J
has the same direction as the velocity of the moving positive charges.3. Drift speed: When an electric field E
is established in a conductor, the charge carriers (assumedpositive) acquire a drift speed vd in the direction of E
; the velocity is related to current density J
as :
dJ (ne)v=
.
4. Resistance of a conductor: If V is the p.d. applied across the conductor and i is the correspondingcurrent, then its resistance is defined as: R = V/i.
5. Change in or R with temperature: If R0 is the resistance of a wire at temperature 0C, thenresistance at any temperature t is t 0R R (1 t)+ , where is the temperature coefficient of resistance. Itcan be defined as t
0
dR1R dt
= .
6. Ohms law: Under given physical conditions the current i produced in the conductor is proportional tothe applied potential difference across the conductor.
7. Combination of cells:i) In series: If n identical cells each of emf and internal resistance r are connected in series, then
current in external resistor R: ninr R
=
+, in case when nr
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For any two junctions RAB in delta is equal to RAB in star, similarly RAC and RBC.9. Meter bridge: It is used to find unknown resistance. If be the balanced length and R is the known
resistance, then unknown resistance 1S R =
.
10. Potentiometer: It is an ideal devise of finding emf of the cells, internal resistance of the cell etc.
If R0 is the resistance of the potentiometer wire, then emf of the cell0
e =
, where is the balancing
length and 0 is the length of the potentiometer wire.
Internal resistance: 1 22
r R
=
, where 1 2and are the balancing lengths without R and with R.
11. Ammeter: Galvanometer of resistance G and full scale deflection current ig can be converted into anammeter of range i by connecting a shunt of resistance S, such that
gSi i
S G=
+
Resistance of ammeter, ASGR
S G=
+
12. Voltmeter: A galvanometer of resistance G and full scale deflection current ig can be converted into avoltmeter of range V by connecting a large resistance R0 in series, such that g 0V i (G R )= + .
R0e
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Thermal and Chemical Effects of Current
1. Electrical appliances: The resistance of any electrical appliance of power Pdesign and Vdesign can be
obtained by:2design
design
VR
P= . The allowable current: design
design
Pi
V= .
2. In houses the electrical appliances are connected in parallel. If appliances of powers P1, P2, areconnected in parallel across the design voltage V, then total power consumed
P = P1 + P2 + .
In series:1 2
1 1 1...
P P P= + +
3. Fuse wire: In a fuse wire, the change in its temperature for the constant current i is given
by2
2 3i
2 r C =
pi. For the given material of fuse wire i2 r3.
4. Chemical effect of direct current:i) Faradays I law: The amount of substance deposited or liberated on any electrode is proportional to
the charge flows in the electrolyte solution. Thus m = zq = z it, where z is called electrochemicalequivalent.
ii) Faradays II law: If same amount of charge flows in two different electrolyte solutions, then theratio of amounts of substances deposited is proportional to their chemical equivalent. Thus
1 1
2 2
m Wm W
= .
5. Faraday constant: W F (1F 96500c / eq)Z
= = .
6. Seebeck effect: The conversion of thermal energy into electrical energy is known as Seebeck effect.
The emf across the junctions of two different metals is given by2bt
at2
= + , where a and b areSeebecks constants.
7. Neutral temperature: It is constant for any thermocouple. Neutral temperaturec i
n n
t t at also t
2 b+
= =
The maximum value of will occur at tn, which is2
max
a
b = .
8. Law of intermediate metal: For thermocouples made of A, B ; B, C and A, CAB BC AC + =
9. Law of intermediate temperature: For any thermocouple [ ] [ ] [ ]3 2 21 3 1
t t tAB AB ABt t t + =
10. Thermoelectric power of Seebeck coefficient: dS a btdt
= = +
11. Peltier coefficient: H dTQ dt
pi = =
.
12. Thomson coefficient: H dSTQ t dt
= =
.
