Identify the correct statement(s) among the following:
(A) If three electrical cells each of emf, E and internal resistance r are connected in series to a resistance R, the current drawn from them is $3E/(R+3r)$.
(B) If these three cells are connected in parallel combination, across resistance R then the current drawn will be $E/(3R+r)$.
(C) If the two cells are connected in series and then one in parallel which are then connected across resistance R, then the current drawn will be $2E/(2R+2r)$.
(D) In a mixed grouping of cells, current will be maximum when total external resistance is equal to total equivalent internal resistance.
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (D) only
(A) Three cells in series: total emf = $3E$, total internal resistance = $3r$.
Current $I = \frac{3E}{R+3r}$ Correct.
(B) Three cells in parallel: equivalent emf = $E$, equivalent internal resistance = $\frac{r}{3}$.
Current $I = \frac{E}{R+\frac{r}{3}} = \frac{3E}{3R+r}$, not $\frac{E}{3R+r}$. Incorrect.
(C) Two in series (emf $=2E$, resistance $=2r$) in parallel with one cell (emf $=E$, resistance $=r$). Equivalent emf is not $2E$ and denominator not $2R+2r$. Incorrect.
(D) For maximum power transfer, external resistance $R =$ equivalent internal resistance $r_{eq}$. Correct.
Correct statements: (A) and (D)