RankLab
Back to Concepts
PhysicsMediumClass 12

Cell Combinations — Series, parallel, mixed

Current Electricity

19

JEE Qs

8%

Hard

75

min

Always correctly determine the equivalent EMF and equivalent internal resistance of the cell combination before applying Ohm's law to the external circuit.

🧮 Key Formulas

V = E - Ir (for cell discharging)
V = E + Ir (for cell charging)
Series combination (n cells): E_eq = Σ E_i, r_eq = Σ r_i (If polarities are same)
Series combination (n identical cells, E, r): E_eq = nE, r_eq = nr
Parallel combination (n identical cells, E, r): E_eq = E, r_eq = r/n
Parallel combination (n non-identical cells, E_1, r_1... E_n, r_n): E_eq/r_eq = Σ(E_i/r_i), 1/r_eq = Σ(1/r_i)
Current for cell combination with external resistance R: I = E_eq / (r_eq + R)
Mixed grouping (m rows, n cells per row, each E, r): E_eq = nE, r_eq = (nr)/m
Condition for maximum power delivered to external resistance R in mixed grouping: nr/m = R

✅ Key Points for JEE

  • 1In series combinations, the equivalent EMF depends on the relative polarities of the cells; opposing cells' EMFs subtract.
  • 2Internal resistances always add up (scalar sum) in series, regardless of EMF polarities.
  • 3For non-identical cells in parallel, the equivalent EMF is a weighted average, and the equivalent internal resistance is calculated like parallel resistors.
  • 4The maximum power transfer theorem applies: maximum power is delivered to an external load when the load resistance equals the equivalent internal resistance of the source (R = r_eq).
  • 5Understand the terminal voltage behavior: V = E - Ir when discharging, V = E + Ir when charging, and V = E if I=0 (open circuit).

⚠️ Common Mistakes

  • Incorrectly handling EMF polarities in series combination (e.g., always adding E_i even if they oppose).
  • Applying the formula for identical cells in parallel to non-identical cells, or vice versa, for equivalent EMF.
  • Forgetting to include the equivalent internal resistance in the denominator when calculating the total current in a circuit (I = E_eq / (R_ext + r_eq)).
  • Confusing the condition for maximum current (R_ext = 0) with the condition for maximum power transfer (R_ext = r_eq).

📝 Practice Questions

See all

Q47.The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A.

2025·NumericalMedium

Q27.Given below are two statements : Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs. Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries. In the light of the above statements, choose the correct answer from the options given below. (1) Both Statement-I and Statement-II are false (2) Statement-I is false but Statement-II is true (3) Both Statement-I and Statement-II are true (4) Statement-I is true but Statement-II is false

2025·Assertion ReasoningMedium

Q34. Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance Rp = 1Ω as shown in the figure. An external resistance of Re = 2Ω is connected via the sliding contact. The electric current in the circuit is : (1) 0.9 A (2) 1.35 A (3) 0.3 A (4) 1.0 A 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

2025·MCQMedium

Q45.Which of the following resistivity ( ρ ) v/s temperature (T) curves is most suitable to be used in wire bound standard resistors? (1) (2) (3) (4)

2025·MCQMedium

Q47.The net current flowing in the given circuit is_______ A.

2025·NumericalMedium

Q30.Refer to the circuit diagram given in the figure. which of the following observations are correct? A. Total resistance of circuit is 6Ω B. Current in Ammeter is 1 A C. Potential across AB is 4 Volts. D. Potential across 2025 (23 Jan Shift 1) JEE Main Previous Year Paper CD is 4 Volts E. Total resistance of the circuit is 8Ω. Choose the correct answer from the options given below: (1) A, B and D Only (2) A, B and C Only (3) A, C and D Only (4) B, C and E Only

2025·MCQMedium

NCERT Chapters

  • Class 12 Physics Ch 3: Current Electricity