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EMF, Internal Resistance, and Terminal Voltage

Understand the concepts of EMF, internal resistance of cells, and how terminal voltage is affected in real circuits.

Why this shows up in the exam

You must distinguish between EMF and terminal voltage and solve related circuit problems in NEET.

How NEET tests this

Numerical · 3 QsDirect recall

Learn the idea

EMF is the maximum potential a cell can give when no current flows; internal resistance r always reduces the usable voltage, so the terminal voltage V equals EMF minus the drop Ir.

🧠 Memory hook: Think of EMF as the cell’s ‘E’nergy source and r as a ‘brake’; the brake always subtracts (‑) from the speed (voltage).

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • EMF (ε) = work done per coulomb when I=0
  • Internal resistance (r) is the opposition inside the cell to the flow of charge
  • Terminal voltage V = ε – I·r
  • If the cell is short‑circuited (R_ext=0) the current I_sc = ε/r
  • In a circuit with external resistance R, the current I = ε/(R+r)

How to approach it

  1. 1Write the loop equation: ε – I·r – I·R = 0
  2. 2Solve for the current I = ε/(R+r)
  3. 3Find terminal voltage using V = ε – I·r or V = I·R
  4. 4For a V‑vs‑I graph, identify slope = –r and y‑intercept = ε

Worked example — watch it click

A student measures the terminal potential difference (V) of a cell (of emf ε and internal resistance r) as a function of the current (I) flowing through it. The slope and intercept of the graph between V and I, then, respectively, equal:

  • ✅- r and ε
  • B)r and - ε
  • C)- ε and r
  • D)ε and - r

The concept behind this problem

The example asks you to read a V‑I straight line; recognizing that the line’s slope is the negative of internal resistance and its intercept is the emf directly tests the V = ε – I r relation.

Step by step

  1. 1Terminal voltage V = ε - Ir.
  2. 2This is equation of straight line V vs I with slope = -r and y-intercept = ε.
  3. 3When I = 0, V = ε (intercept).
  4. 4The slope dV/dI = -r.

Watch out

A common mistake is to write the slope as +r or to claim the intercept is –ε.

Common slip-ups that cost marks

  • •Mixing up EMF with terminal voltage – they are equal only when I=0
  • •Taking the slope as +r instead of –r in the V‑I straight line
  • •Forgetting the internal resistance when the external resistor is very small

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 4NEET 2024

The terminal voltage of the battery, whose emf is 10 V and internal resistance 1 Ω, when connected through an external resistance of 4 Ω as shown in the figure is:

Push further

More challenging

6 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 6

A cell with an electromotive force (emf) of 12 V and an internal resistance of 0.5 Ω is connected to an external resistor of 5.5 Ω. What is the terminal voltage across the external resistor?

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