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Definition: The device which converts chemical energy into electrical energy is known as electric cell. Battery is a host of constant emf but not constant current.
Emf of cell (E): The potential difference across the terminals of a cell when it is not supplying any current is called it's emf.
Potential difference (V): The voltage across the terminals of a cell when it is supplying current to external resistance is called potential difference or final voltage. Potential energy difference is same to the product of current and resistance of that given part i.e. V = iR.
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Internal resistance (r): In case of a cell the opposition of electrolyte to the flow of current through it is called internal resistance of the cell. The internal resistance of a battery relays on the distance between electrodes (r ∝ d), area of electrodes [r ∝ (1/A)] and nature, concentration (r ∝ C) and temperature of electrolyte [r ∝ (1/temp)].
A cell is called ideal, if it has zero internal resistance.
Closed Circuit
Cell gives a constant current in the circuit.
(i) Current given by the cell i = E/R+r
(ii) Potential energy difference among the resistance V = iR
(iii) Potential drop inside the cell = ir
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(iv) Equation of cell E = V + ir
(v) Internal resistance of the cell r = (E/V-1)R
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(vi) Power dissipated in external resistance (load)  ,
Power delivered will be maximum when R = r so  .
This statement is generalized from is called "maximum power transfer theorem".
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(vii) When the cell is being charged i.e. current is given to the cell then E = V - ir and E < V.
Open Circuit: When no current is going from the cell it is aid to be in open circuit
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(i) Current through the circuit i = 0
(ii) Potential difference between A and B,
(iii) Potential difference between C and D,
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Short Circuit
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If two ends of battery are join together by a thick conducting wire
(i) Maximum current (called short circuit current) flows momentarily isc=E/r
(ii) Potential difference V = 0
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Grouping of Cells
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Group of cell is called a battery: In series grouping of cell's their emf's are additive or subtractive while their internal resistances are always additive. If dissimilar rods of batteries are connected together their emf's are added to each other while if their similar plates are connected together their emf's are subtractive.
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Series Grouping: In series grouping anode of one cell is connected to cathode of other cell and so on. If n similar cells are connected in series
(i) Equivalent emf of the combination Eeq = nE
(ii) Equivalent internal resistance req = nr
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(iii) Main current = Current from each cell i = nE/R+nr
(iv) Potential energy difference across external resistance V = iR
(v) Potential difference across every battery V′ = V/n
(vi) Power loss in the external circuit (nE/R+nr)2R
(vii) Condition of maximum power R = nr
(viii) This kind of combination is used when nr < < R.
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Parallel Grouping: In parallel grouping all anodes are connected at one point and all cathodes are connected together at other position. If n identical cells are connected in parallel
(i) Equivalent emf Eeq = nE
(ii) Equivalent internal resistance req = r/n
(iii) Main current i = E/R+r/n
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(iv) Potential difference across external resistance = p.d. across each cell = V = iR
(v) Current from each cell i′=i/n
(vi) This kind of combination is needed when nr > > R
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Mixed Grouping: If n similar type cells are connected in a row and such m row's are connected in parallel as shown.
(i) Equivalent emf of the combination Eeq =nE
(ii) Equivalent internal resistance of the relation req = nr/m
(iii) main current going through the load 
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(iv) Potential difference across load V = iR
(v) Potential energy difference among each battery v′ = v/n
(vi) Current from each cell i′ = i/n
(vii) Condition for maximum power 
(viii) Total number of cell = mn
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