Cells in Series: Equivalent EMF and Internal Resistance
Physics · Current Electricity · NEET
When cells are joined in series (positive terminal of one to negative of the next), the equivalent EMF adds up and the equivalent internal resistance adds up: E_eq = E1 + E2 + ... and r_eq = r1 + r2 + ... . Memory hook: "Series stacks everything" - both EMF and resistance grow. If a cell is reversed (opposing), subtract its EMF, but its resistance still adds.
Two cells in series between A and C behave as one cell with E_eq = E1 + E2 and r_eq = r1 + r2. The same current passes through both cells; if a cell is reversed, subtract its EMF but still add its resistance.
Your doubts, answered
Do the EMFs add up when cells are in series?
Yes. For cells connected the normal way (positive of one to negative of the next), E_eq = E1 + E2 + ... . Two 1.5 V cells in series give 3 V. This is why a torch with 2 or 4 cells gives more voltage - the EMFs stack. NCERT states the equivalent EMF of a series combination is just the sum of the individual EMFs.
Does the internal resistance also add up in series?
Yes, always. r_eq = r1 + r2 + ... . This is true even for a reversed (opposing) cell. Resistance is a property of the material and never becomes negative, so it keeps adding no matter which way the cell faces. Only the EMF can carry a minus sign.
What if one cell is connected in reverse (opposing)?
Then its EMF enters the sum with a minus sign: E_eq = E1 - E2 (if cell 2 opposes cell 1). But the internal resistance still adds: r_eq = r1 + r2. Example: a 6 V cell and a reversed 4 V cell give E_eq = 6 - 4 = 2 V, with r_eq = r1 + r2. This is a very common NEET trap.
Why doesn't short-circuit current change with more series cells?
For n identical cells (EMF E, internal resistance r) in series, E_eq = nE and r_eq = nr. On short circuit, I = E_eq / r_eq = nE / nr = E/r. The n cancels, so the current stays the same no matter how many cells you stack. This exact idea was asked in NEET 2018.
When should I use series instead of parallel for cells?
Use series when you need a higher voltage (EMFs add). Use parallel when you need to drive more current for longer with the same voltage (internal resistance drops). For NEET, remember: series boosts EMF, parallel boosts current capacity.
⚠️ The NEET trap ✗ Adding EMFs but forgetting that internal resistance also adds, or taking the average EMF for two cells in series. ✓ In series both add: E_eq = E1 + E2 and r_eq = r1 + r2. EMF is a sum, never an average. For a reversed cell, subtract its EMF but still add its resistance. 🧠 Series = SUM, not average. EMF can go minus (if reversed); resistance never can.
Real NEET questions
NEET 2018
A battery of n identical cells (each of EMF E and internal resistance r) connected in series is short-circuited and the current I is measured. Which graph correctly shows I versus n?
A · A rising curve that saturates
B · A straight line through the origin
C · A horizontal line (I constant, independent of n) ✓
D · A decaying curve
Solution: Step 1: For n identical cells in series, equivalent EMF E_eq = nE. Step 2: Equivalent internal resistance r_eq = nr. Step 3: On short circuit the external resistance is zero, so current I = E_eq / r_eq = nE / (nr). Step 4: The n cancels, giving I = E/r, which does not depend on n. So the graph of I versus n is a horizontal line. Correct option: C.
Solved Current Electricity NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the formula for equivalent EMF of cells in series?
E_eq = E1 + E2 + E3 + ... , the algebraic sum of the individual EMFs. If a cell is reversed, its EMF is taken as negative.
What is the equivalent internal resistance of cells in series?
r_eq = r1 + r2 + r3 + ... , the simple sum of all internal resistances. It always adds, even for a reversed cell.
How does a series combination of cells behave overall?
The whole combination acts like a single cell of EMF E_eq = E1 + E2 + ... and internal resistance r_eq = r1 + r2 + ... connected to the external circuit.
For n identical cells in series driving resistance R, what is the current?
I = nE / (R + nr), where E is each cell's EMF and r its internal resistance. When R = 0 (short circuit), I = E/r.
Why do we connect cells in series in devices?
To get a higher voltage, because the EMFs add up. Many electronic devices need more than one cell's worth of EMF, so cells are stacked in series.
