two cells of emf 10V and 2V and internal resistances 10 ohm and 5ohm respectively are connected in parallel.find the effective voltage across R.
please explain stepwise with formulae....

Dear Student,

Please find below the solution to the asked query:

Given situation is drawn in the following diagram.

So, the circuit can be simplified to a state, where a single cell of emf and a single internal resistance can be placed between A and B. Here, the question is to calculate V_AB.
So, from effective resistance formula,
$\frac{1}{R_{eff}} = \frac{1}{R_1}+\frac{1}{R_2} = \frac{1}{10}+\frac{1}{5} = \frac{1+2}{10}\Rightarrow R_{eff} = \frac{10}{3} \Omega$
from effective emf formula,
$$\begin{gathered} I_{eff} = I_1 + I_2 \\ \Rightarrow \frac{V_{eff}}{R_{eff}} = \frac{V_1}{R_1} + \frac{V_2}{R_2} \Rightarrow \frac{V_{eff}}{{\displaystyle \raisebox{1ex}{$10$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}} = \frac{10}{10}+\frac{2}{5} \Rightarrow V_{eff} = \left(\frac{10}{3}\right)\left(\frac{7}{5}\right) \\ \Rightarrow V_{eff} = \frac{14}{3} = 4.67 V \end{gathered}$$
Therefore, $V_{AB} = 4.67 V$



Hope this information will clear your doubts about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards