Physics Current Electricity

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Current Electricity

Grouping of cells

Group of cells is called Battery. Cells are usually grouped in following ways.
In series grouping of cell's their emfs are additive or subtractive while their internal resistances are
always additive. If dissimilar plates of cells are connected together their emfs are added to each other
while if their simi lar plates are connected together their emfs are subtractive.

Group of cells is called Battery. Cells are usually grouped in following ways.
In series grouping of cell's their emfs are additive or subtractive while their internal resistances are
always additive. If dissimilar plates of cells are connected together their emfs are added to each other
while if their simi lar plates are connected together their emfs are subtractive.

`text( Series grouping : )`

In series grouping anode of one cell is connected to cathode of other cell and so
on. Ifn identical cells are connected in series.

(i) Equivalent emf of the combination `E_(eq) = nE`
(ii) Equivalent internal resistance `r_(eq) = nr`
(iii) Main current= Current frorn each cell `= I= (nE/(R + nr))`
(iv) Potential difference across external resistance `V = iR`
(v) Potential difference across each cell `v' = v/n`
(vi) Power dissipated in the external circuit `= ( (nE)/(R+nr)^2.) R`
(vii) Condition for maximum power `R = nr` and `P_(max) = n(E^2 / 4r)`
(viii) This type of combination is used when `nr << R.`

In series grouping of cell's their emfs are additive or subtractive while their internal resistances are
always additive. If dissimilar plates of cells are connected together their emfs are added to each other
while if their similar plates are connected together their emfs are subtractive.

In series grouping anode of one cell is connected to cathode of other cell and so
on. Ifn identical cells are connected in series.

(i) Equivalent emf of the combination `E_(eq) = nE`
(ii) Equivalent internal resistance `r_(eq) = nr`
(iii) Main current= Current frorn each cell `= I= (nE/(R + nr))`
(iv) Potential difference across external resistance `V = iR`
(v) Potential difference across each cell `v' = v/n`
(vi) Power dissipated in the external circuit `= ( (nE)/(R+nr)^2.) R`
(vii) Condition for maximum power `R = nr` and `P_(max) = n(E^2 / 4r)`
(viii) This type of combination is used when `nr << R.`

In series grouping of cell's their emfs are additive or subtractive while their internal resistances are
always additive. If dissimilar plates of cells are connected together their emfs are added to each other
while if their similar plates are connected together their emfs are subtractive.

Parallel grouping

In parallel grouping all anodes are connected at one point and all cathode are
connected together at other point. lf n identical cells are connected in parallel.

(i) Equivalent emf `E_(eq) = E`
(ii) Equivalent internal resistance `R_(eq) = r/n`
(iii)Main current `i = E/( R + r / n)`
(iv) potential difference across external resistance `e = p.d`. across each cell `V = iR`
(v)Current from each cell `i' = i/n`
(vi) Power dissipated in the circuit `P = (E/(R+r/n) )^2 . R`
(vii) Condition for max. power is `R = r/n` and `P_(max) = n(E^2 / 4r)`
(viii) This type of combination is used when `nr>> R`

In parallel grouping all anodes are connected at one point and all cathode are
connected together at other point. lf n identical cells are connected in parallel.

(i) Equivalent emf `E_(eq) = E`
(ii) Equivalent internal resistance `R_(eq) = r/n`
(iii)Main current `i = E/( R + r / n)`
(iv) potential difference across external resistance `e = p.d`. across each cell `V = iR`
(v)Current from each cell `i' = i/n`
(vi) Power dissipated in the circuit `P = (E/(R+r/n) )^2 . R`
(vii) Condition for max. power is `R = r/n` and `P_(max) = n(E^2 / 4r)`
(viii) This type of combination is used when `nr>> R`

Mixed Grouping

lf `n` identical cell's are connected in a row and such m row's are connected in
parallel as shown.
(i) Equivalent emf of the combination `E_(eq) = nE`
(ii) Equivalent internal resistance of the combination `r_(eq)= nr/m`
(iii) Main current flowing through the load `i = (nE)/ (R + (nr/m)) = mnE/(mR+nr)`
(iv) Potential difference across load `V = iR`
(v) Potential difference across each cell `V'= V/n`
(vi)Current from each cell `i' = i/n`
(vii) Condition for maximum power `R =nr/m` and `P_(max) = (mn)E^2 / 4r`
(viii) Total number of cell `= mn`

lf `n` identical cell's are connected in a row and such m row's are connected in
parallel as shown.
(i) Equivalent emf of the combination `E_(eq) = nE`
(ii) Equivalent internal resistance of the combination `r_(eq)= nr/m`
(iii) Main current flowing through the load `i = (nE)/ (R + (nr/m)) = mnE/(mR+nr)`
(iv) Potential difference across load `V = iR`
(v) Potential difference across each cell `V'= V/n`
(vi)Current from each cell `i' = i/n`
(vii) Condition for maximum power `R =nr/m` and `P_(max) = (mn)E^2 / 4r`
(viii) Total number of cell `= mn`

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