Consider four cells, each of emf ε and internal resistance r. Arrange them in the decreasing order of equivalent emf if they are connected in four different ways as per statements given below:
(A) Two cells are connected in parallel and then they are connected with the remaining two already connected in series.
(B) All four are connected in parallel
(C) All four are connected in series
(D) Three are connected in parallel and the fourth is then connected in series with them.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (C), (A), (D), (B)
Series connection adds emfs; identical cells in parallel give the emf of a single cell (only the internal resistance changes). Find the equivalent emf of each arrangement:
(A) Two cells are connected in parallel and then they are connected with the remaining two already connected in series. — \( \varepsilon\ (\text{parallel pair}) + 2\varepsilon\ (\text{series pair}) = 3\varepsilon \)
(B) All four are connected in parallel — \( \varepsilon \)
(C) All four are connected in series — \( 4\varepsilon \)
(D) Three are connected in parallel and the fourth is then connected in series with them. — \( \varepsilon\ (\text{three in parallel}) + \varepsilon = 2\varepsilon \)
Decreasing order: \( 4\varepsilon \gt 3\varepsilon \gt 2\varepsilon \gt \varepsilon \), that is (C), (A), (D), (B).