Internal Resistance of cell & Combinations of Cells By R. S. Saini. (M.Sc. Physics, M.Ed.) Kendriya Vidyalaya, Sector 47, Chandigarh

Transcription

1 ntenal Resistance of cell & Combinations of Cells By R. S. Saini (M.Sc. Physics, M.d.) Kendiya idyalaya, Secto 47, Chandigah

2 Souces of emf: The electo motive foce is the maximum potential diffeence between the two electodes of the cell when no cuent is dawn fom the cell. Compaison of MF and P.D: MF MF is the maximum potential diffeence between the two electodes of the cell when no cuent is dawn fom the cell i.e. when the cicuit is open. t is independent of the esistance of the cicuit. The tem emf is used only fo the souce of emf. t is geate than the potential diffeence between any two points in a cicuit. Potential Diffeence P.D is the diffeence of potentials between any two points in a closed cicuit. t is popotional to the esistance between the given points. t is measued between any two points of the cicuit. Howeve, p.d. is geate than emf when the cell is being chaged.

3 ntenal Resistance of a cell: The opposition offeed by the electolyte of the cell to the flow of electic cuent though it is called the intenal esistance of the cell. Factos affecting ntenal Resistance of a cell: i) Lage the sepaation between the electodes of the cell, moe the length of the electolyte though which cuent has to flow and consequently a highe value of intenal esistance. ii) Geate the conductivity of the electolyte, lesse is the intenal esistance of the cell. i.e. intenal esistance depends on the natue of the electolyte. iii) The intenal esistance of a cell is invesely popotional to the common aea of the electodes dipping in the electolyte. iv) The intenal esistance of a cell depends on the natue of the electodes. = + v = R + = (R + ) = / (R + ) This elation is called cicuit equation. R v

4 ntenal Resistance of a cell in tems of, and R: = + v = + = - Dividing by R =, v R = R = ( - 1) R Detemination of ntenal Resistance of a cell by voltmete method: + + R.B (R) K Open cicuit (No cuent is dawn) MF () is measued R.B (R) K Closed cicuit (Cuent is dawn) Potential Diffeence () is measued

5 Cells in Seies combination: Cells ae connected in seies when they ae joined end to end so that the same quantity of electicity must flow though each cell. NOT: 1. The emf of the battey is the sum of the individual emfs 2. The cuent in each cell is the same and is identical with the cuent in the entie aangement. 3. The total intenal esistance of the battey is the sum of the individual intenal esistances. R Total emf of the battey = n (fo n no. of identical cells) Total ntenal esistance of the battey = n Total esistance of the cicuit = n + R Cuent = n n + R (i) f R << n, then = / (ii) f n << R, then = n ( / R) Conclusion: When intenal esistance is negligible in compaison to the extenal esistance, then the cells ae connected in seies to get maximum cuent.

6 Cells in Paallel combination: Cells ae said to be connected in paallel when they ae joined positive to positive and negative to negative such that cuent is divided between the cells. NOT: 1. The emf of the battey is the same as that of a single cell. 2. The cuent in the extenal cicuit is divided equally among the cells. 3. The ecipocal of the total intenal esistance is the sum of the ecipocals of the individual intenal esistances. Total emf of the battey = Total ntenal esistance of the battey = / n R Total esistance of the cicuit = ( / n) + R Cuent = n nr + (i) f R << /n, then = n( / ) (ii) f /n << R, then = / R Conclusion: When extenal esistance is negligible in compaison to the intenal esistance, then the cells ae connected in paallel to get maximum cuent.

7 Mixed Gouping Cells ae said to be in mixed gouping if ae connected in the manne as shown.

8 Mixed Gouping Let n be the no. of cells in seies in each ow and m be the no. of such ows. Let be the e.m.f. of each cell and be the intenal esistance of each cell. n each ow, thee ae n cells in seies, theefoe thei total esistance is n and total e.m.f. in n. Thus ae m ows of cells in paallel, theefoe total intenal esistance of all the cells is given by m = + + ( m tems) = n n n n p

9 Mixed Gouping Hence total esistance in the cicuit is = and effective e.m.f. is = n n m Hence total cuent n mn = = (1) n R + mr + n m Fo cuent to be maximum mr + n should be minimum which can be poved to be minimum when mr = n as follows

10 Mixed Gouping ( ) ( ) ( ) ( ) ( ) mr + n = mr + n = mr + n 2 ml n + 2 ml n = mr n + 2 mr n Which is minimum when mr n = 0 o mr = n And maximum cuent is given by max m n = = 2 2R