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) 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 \( 3E/(R+3r) \). — Correct. In series the emfs and the internal resistances add.
\( \displaystyle I = \frac{3E}{R + 3r} \)
(B) If these three cells are connected in parallel combination, across resistance R then the current drawn will be \( E/(3R+r) \). — Incorrect. In parallel the emf stays \( E \) and the internal resistance becomes \( r/3 \).
\( \displaystyle I = \frac{E}{R + r/3} = \frac{3E}{3R + r} \neq \frac{E}{3R + r} \)
(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 \( 2E/(2R+2r) \) — Incorrect. The branches (\( 2E, 2r \)) and (\( E, r \)) in parallel give
\( \displaystyle E_{\mathrm{eq}} = \frac{2E/2r + E/r}{1/2r + 1/r} = \frac{4E}{3} \qquad r_{\mathrm{eq}} = \frac{2r \times r}{2r + r} = \frac{2r}{3} \)
\( \displaystyle I = \frac{4E/3}{R + 2r/3} = \frac{4E}{3R + 2r} \neq \frac{2E}{2R + 2r} \)
(D) In a mixed grouping of cells, current will be maximum when total external resistance is equal to total equivalent internal resistance. — Correct. For \( m \) rows of \( n \) cells in a mixed grouping:
\( \displaystyle I = \frac{m n E}{m R + n r}, \qquad I \text{ is maximum when } R = \frac{n r}{m} \)
Statements (A) and (D) are correct, which is Option (2).