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Current:- Current strength, in a conductor, is defined as the rate of flow of charge across any cross section of the conductor.
I= q/t = ne/t
For non-uniform flow,
I= dq/dt
Or, q = ? I dt
(a) C.G.S. electro-static unit (esu):- 1 esu of current (stat-ampere) = 1 esu of charge/1 second
(b) C.G.S. electro-static unit (emu):- 1 emu of current (ab-ampere) = 1 emu of charge/1 second
(c) S. I unit (ampere):- 1 ampere = 1 coulomb/1 second
(d) 1 A = 3×10^{9}esu of current or stat-ampere
(e) 1 A = 1/10 emu of current or abampere
V = (eV/ml)
Here, e is the charge of electron, V is the potential difference, m is the mass and is the relaxation time.
Electric current and Drift velocity:- I= q/t = nAve
Ohm’s Law for conductors:- At constant temperature current flowing through a conductor of uniform area of cross-section, is proportional to the difference of potential across its terminals.
(a) V = IR , Here, R = (ml/nAe^{2}) (1/)
(b) R=ρl/A
(c) ρ = 1/σ
(d) v_{d} = (qE/m)
(e) I = neAv_{d}
(f) ρ = m/ne^{2}
(g) σ = ne^{2}/m
R= V/I
(a) In S.I:- 1 ohm = 1 volt/1 ampere
(b) In C.G.S system:-
1 statohm = 1 statvolt/1 statamp
1 abohm = 1 abvolt/1 abampere
(c) Relation between ohm and statohm:- 1 ohm = (1/9×10^{11}) statohm
(d) Relation between ohm and abohm:- 1 ohm = 10^{9}abohm
Temperature coefficient of resistance (α) is defined as change in resistance of the conductor per unit resistance per degree centigrade rise of temperature.
R_{t}=R_{0}[1+α(T-T_{0})]
α = R_{t }- R_{0}/R_{0}(T-T_{0})
Here, R_{t},R_{0} is the resistance of the conductor at tº C and 0º C respectively.
Here R is the resisteance of the conductor, A is cross sectional area of conductor and l is the length of the conductor
ρ = m /ne^{2}
(a) Conductors:-
ρ_{t} = ρ_{0} [1+α(T-T_{0})]
Here c is called the temperature coefficient of the resistivity.
= (ρ_{t} - ρ_{0}) /ρ_{0} (T--T_{0})
Temperature coefficient of resistivity of a conductor is defined as the change in resistivity per unit resistivity per degree Celsius rise of temperature.
α=ρ_{t} - ρ_{0}
(b) Insulators:-
σ = 1/ρ
Unit:- ohm^{-1}m^{-1}
Conductance = 1/R = (1/ρ) (A/l)
Unit:- mho or ohm^{-1}m^{-1}
(a) J = I/A
(b) J = nev_{d}
(c) J =σE
(d) µ = v_{d}/E
(e) σ = neµ
?
Thus, electrical conductivity can also be defined as electric current density per unit electric field strength.
(a) R = R_{1}+R_{2}+R_{3}
(b) V = V_{1}+V_{2}+V_{3}
(c) I = I_{1} = I_{2} = I_{3 }= Constant
(d) V_{1} = IR_{1}, V_{2} = IR_{2}, V_{3} = IR_{3}
(a) 1/R = 1/ R_{1} + 1/ R_{2} +1/ R_{3}
(b) I = I_{1}+I_{2}+I_{3}
(c) V = V_{1} = V_{2} = V_{3 }= Constant
(d) I_{1} = V/R_{1}, I_{2} = V/R_{2}, I_{3} = V/R_{3}
(a) I_{1} = I (R_{2}/R_{1}+R_{2})
(b) I_{2} = I (R_{1}/R_{1}+R_{2})
In general,
Current in one branch = total current × (resistance of second branch / sum of resistances in the two branches)
(a) Cells in series:-
I= (nE)/(R+nr)
If R<<nr, then I = E/R
If R>>nr, then I = nE/R
(b) Cells in parallel:-
I= E/[R+(r/m)]
If R>>r/m, then I = E/R
If R>>r/m, then I = m(E/R)
(c) Mixed grouping:-
(a) I = mnE/(mR+nr)
(b) I is maximum when nR = mR
(c) I_{max} = mnE/(2√mnrR)
The electromotive force E of a cell is defined as the difference of potential between its terminals when there is no current in the external circuit, i.e., when the cell is in open circuit.
The potential difference of a cell is the difference of potential between two terminals when it is in closed circuit.
E = V+IR
r = R (E-V/V)
(a) P = VI
(b) P = I^{2}R = V^{2}/R
Unit of power:-1 watt = 1 volt × 1 amp
W = Vq = V(It)
Unit of electric energy:-
1 joule = 1 watt sec
1 kilowatt hour = 1000 watt hour
(a) The mass of ion deposited on an electrode in the process of electrolysis, is proportional to the quantity of charge that has passed through the electrolyte.
m = Zq = ZIt
(b) When same current passes through several electrolytes for the same time, the masses of various ions deposited at each of the electrodes are proportional to their chemical equivalents (equivalent weights).
m/W = constant
Or, Z_{1}/Z_{2} = W_{1}/W_{2}
So, W/Z = constant = F
I = I^{2}Rt Joule = I^{2}Rt/J Calorie
(a) Resistance of filament, R = V^{2}/P
(b) Maximum current that can be allowed to pass through bulb, I_{max} = P/V
P = P_{1}+P_{2}+P_{3}
1/P= 1/P_{1}+1/P_{2}+1/P_{3}
R_{2}/R_{1} = (l_{1}/l_{2}) (A_{1}/A_{2}) = (l_{2}/l_{1})^{2} = (A_{1}/A_{2})^{2} = (r_{1}/r_{2})^{4} [Since, l_{1} A_{1} = l_{2} A_{2}]
Thermo e.m.f:-e = αθ + (βθ^{2}/2) (Here, θ = θ_{H} = θ_{C})
Neutral temperature: θ_{N} = -(α/β)
Temperature of inversion:- θ_{N} = (θ_{1} + θ_{C})/2 [Since, θ_{1} – θ_{N} = θ_{N} – θ_{C}]
Thermoelectric power or Seebeck Coefficient:- S =de/dθ = α +βθ
Peltier effect:-
Heat absorbed per second at a junction when a current I flows = πI
Here π is Peltier coefficient and is given by, π = Sθ_{H}
σ = (ΔQ/time)/IΔθ
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