. C ELLS IN S ERIES AND IN P ARALLEL Like resistors, cells can be combined together in an electric circuit. And like resistors, one can, for calculating currents and voltages in a circuit, replace a combination of cells by an equivalent cell. FIGURE .
Two cells of emf’s ε and ε in the series. r , r are their internal resistances. For connections across A and C, the combination can be considered as one cell of emf ε eq and an internal resistance r eq . Consider first two cells in series (Fig.
. ), where one terminal of the two cells is joined together leaving the other terminal in either cell free. ε , ε are the emf’s of the two cells and r , r their internal resistances, respectively. Let V (A), V (B), V (C) be the potentials at points A, B and C shown in Fig.
. . Then V (A) – V (B) is the potential difference between the positive and negative terminals of the first cell. We have already calculated it in Eq.
( . ) and hence, AB (A) – (B) – I r ≡ ( . ) Similarly, BC (B)– (C) – I r ≡ ( . ) Hence, the potential difference between the terminals A and C of the combination is ( ) ( ) ( ) ( ) AC (A) – (C) A – B B – ≡