Current Electricity

Current Electricity

• Current density ():
  
  The current density at any point inside a conductor is defined as a vector quantity whose magnitude is equal to current per unit infinitesimal area at that point, the area held normal to the direction of flow of current.
  Current density points along the direction of current flow. If A_n is small area normal to Current I, then current density =
  The unit of current density is Am^-2 from above, we have I = JA cos =
• Drift Velocity :
  
  When no potential difference is applied across a conductor, the free electron are in random motion and hence the average velocity of free electrons is zero and consequently this motion doesn't constitute a net transport of charge across any section of conductor and so no current flows in the conductor.
  
  On application of potential difference across a conductor, the electrons gain some average velocity in the direction of positive potential. This average velocity in addition to random velocity of electrons is called Drift Velocity (v_d).
• Drift speed of electrons in a conductor.
  The drift speed of electrons in a conductor through which a current 'I' flows is given by ; where 'n' is the number of electrons per unit volume of conductor, 'e' is electronic charge and 'A' is the cross sectional area of conductor.
• EMF of a cell :
  The work done in carrying a unit positive charge once in the circuit including the cell is defined as the electro motive force. E =
• It is the difference of potential between the terminals of a cell in open circuit and is responsible for the flow of current in a circuit.
  
  Internal resistance of a cell :
• It is the resistance offered by the electrolyte of the cell.
• It depends on (i) r a area of electrodes (ii) r d, d - distance (iii) nature of electrolyte (iv) area of cross section of the electrolyte through which the current flows. (v) concentration (vi) temp of electrolyte (r ).
• Internal resistance of ideal cell is zero.
• Power transferred to the load is maximum when external resistance becomes equal to internal resistance.
• Terminal Pd of cell :
• It is P.D. between the terminals of cell when it is in closed circuit.
• Terminal P.D. of cell when cell being discharged is V = E -ir
  P.D. = iR
  i = circuit current
  r = Internal resistance of cell
  R = External resistance
• Terminal P.D. of cell during charging is V = E + ir
  
  Ohm's law :
• At constant temperature, the current 'i' through a conductor is proportional to P.D. 'V' across its ends V = iR (or) R =
  
  Resistance : R
• The property of substance by virtue of which it opposes the flow of current through it, is known as the resistance.
• For a conductor if length of a conductor, A = area of cross-section of conductor,
  n = No. of free electrons per unit volume in conductor,
  R =
  Where = resistivity of the material of conductor.
  Conductivity : (or)
  specific conductance : ()
• It is reciprocal of resistivity. =
  
  Variation of resistance with temperature :
• R_t= R₀(1 + t) or
  
  =
  R_t= Resistance at t°C
  R₀= Resistance at 0°C
  = Temperature coefficient of resistance.
  
  KIRCHHOFF'S RULE :-
• All electrical networks can't be reduced to simple series parallel combinations. Kirchhoff gave two simple and general rules which can be applied to find current flowing through (or) voltage drops across resistances in such complex networks.
  First Rule : (Junction Rule)
  The sum of all incoming and outgoing currents from a junction is zero
  Second Rule : (loop Rule)
  a) The algebraic sum of changes of potential (potential rise and drop) across the elements of a circuit in a closed loop is zero. This rule follows from law of conservation of energy.
  E₂ + I₃R₃+ I₂R₂= 0
  
  solving these three equation I₁, I₂and I₃can be obtained.
  
  Wheatstone's Bridge :
• Wheatstone bridge is an arrangement of four resistance which can be used to measure one of them in terms of rest. Arms AB and BC are called ratio arm and arms AC and BD are called conjugate arms.
  
  
  Potentiometer :
• Potentiometer is a device mainly used to measure emf of a given cell and to compare emf's of a given cell and to compare emf's of cells. It is also used to measure internal resistance of a given cell. It works on constant potential gradient and null deflection method.