My TB gives the following formula of emf of cells in parallel:
$$\frac V{R_{eq}} = \frac{V_1}{R_1} + \frac{V_2}{R_2}+\frac{V_3}{R_3}+…$$
where
$\frac 1{R_{eq}} = \frac 1{R_1} + \frac 1{R_2}+\frac 1{R_3}+…$
$R_1, R_2, R_3, …$ are the internal resistances
$V_1, V_2, V_3, …$ are the individual emfs
How can this be proven? How can the equivalent resistance be calculated when the voltages across the resistors are different?
Best Answer
Yes, Kirchhoff's laws are valid here and also valid for any circuit in general.
The proof for this is quite simple and elegant
For n cell with individual internal resistances(represented in figure II) , we can assume an equivalent cell (represented in figure I)
We then equate the individual currents in each cell branch to the net current in the equivalent circuit using Kirchhoff's junction rule
We then apply Kirchhoff's voltage rule for each individual branch runing across the whole circuit, obtaining the individual current expressions
We then put in the current expressions in the junction rule expression and Voila! Done.