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What is called series connection of cell ? Derive equation of equivalent emf of two cell with emfepsilon_(1) and epsilon_(2) connected in series. |
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Answer» <P> Solution :`rArr `When one terminal of two cell connected with each other and another terminal of each cell are kept free then such connection is called series connection of cell. `rArr` In figure, battery having emf `epsilon_(1)` and internal resistance `r_(1)` is connected between A arid B and battery with emf `epsilon_(1)` and internal resistance `r_(2)` is connected between B and C. `rArr ` Let equivalent emf between A and C be `E_(eq)` and equivalent resistance of `r_(1) and r_(2)` be `r_(eq)` . `rArr ` Let potential at point A, B and C be V(A), V(B) and V(C) respectively. P .d. between positive and negative terminal of frist cell `V_(AB) = V(A) - V(B)` . `rArr ` p.d. between positive and negative terminal of second cell = V(B) - V(C). `V(A) - V(B) = epsilon_(1) - Ir_(1) ""` ... (1) `V(B) - V(C)= epsilon_(2) - Ir_(2) "" `... (2) `rArr` p.d. between A and C , `V_(AC) = V_(AB) + V_(BC)` = [V(A) - V(B)) + [V(B) - V(C)] `= epsilon_(1)- Ir_(1) + epsilon_(2) - Ir_(2) ` = ` epsilon_(1) + epsilon_(2) - Ir_(1) - Ir_(2)` ` = epsilon_(1) + epsilon_(2) - I(r_(1) + r_(2)) "" ` ... (3) For given combination equivalent emf between A and C be `e_(eq)` and internal resistance `r_(eq)` , `V_(AC) = V(A) - V(C) = e_(eq) - Ir_(eq) "" `... (4) Comparing (3) and (4) , `e_(eq) = epsilon_(1) + epsilon_(2)` and `r_(eq) - r_(1) + r_(2)` If cells are connected in series in opposing CONDITION then, `V_(BC) = V(B) - V(C) ` = `epsilon_(2) - Ir_(2)` `therefoe e_(eq)= epsilon_(1) - epsilon_(2)"" (epsilon_(1) gt epsilon_(2))` `rArr` If .n. cells are connected in series helping condition then, `epsilon_(eq) = epsilon_(1) + epsilon_(2) + ... epsilon_(n)` equivalent internal resistarice of combination will be equal to summation of individual internal resistance of each cell `r_(eq) = r_(1) + r_(2) + ... + r_(n)` If given cell is connected in opposing condition then emf of given cell will be considered as negative. |
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