# EMF and Internal Resistance > EMF and internal resistance for NEET Physics: terminal voltage, maximum power transfer, cells in series and parallel, efficiency numericals. - Canonical URL: https://prepelephant.com/topics/neet-ug/physics/emf-and-internal-resistance - Exam / course: NEET-UG · Subject: Physics - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "EMF and Internal Resistance", PrepElephant, https://prepelephant.com/topics/neet-ug/physics/emf-and-internal-resistance ## Direct answer Every real cell keeps a small resistance r inside, so the voltage at its terminals falls as soon as current flows: V = ε - Ir while discharging, V = ε on open circuit, and V = ε + Ir while being charged, with the circuit current I = ε/(R + r). The emf itself is the chemistry's work per coulomb, unaffected by the load. This bookkeeping decides three NEET favourites: maximum power reaches the external resistance exactly when R = r; the efficiency of transfer is η = R/(R + r), only 50 per cent at maximum power; and identical cells combine as ε_eq = nε, r_eq = nr in series but ε, r/n in parallel. ## What you must remember - **Terminal voltage:** V = ε - Ir while discharging; the drop Ir is spent inside the cell; a battery tester reads full voltage only because it draws negligible current. - **Charging case:** V = ε + Ir — the charger pushes against both the emf and the internal drop. - **Circuit current:** I = ε/(R + r); short-circuiting the cell gives I = ε/r, large because r is small — why even a low-voltage cell is dangerous when shorted. - **Maximum power transfer:** P_max = ε^2/4r when R = r; beyond this point delivered power falls while efficiency keeps rising — the two optima are different. - **Efficiency:** η = R/(R + r); power transfer capability and efficiency pull in opposite directions, and questions probe which one is being maximised. - **Cells in series:** ε_eq = nε, r_eq = nr — higher voltage, higher internal resistance. - **Cells in parallel (identical):** ε_eq = ε, r_eq = r/n — same voltage, lower internal resistance, longer life. ## A 12-volt cell under three loads Take a cell of ε = 12 V and r = 1 Ω. Across R = 5 Ω: I = 12/6 = 2 A, terminal voltage V = ε - Ir = 10 V, and of the 24 W generated, 20 W reaches the load while 4 W heats the cell — efficiency 5/6 ≈ 83 per cent. Now replace the load with R = 1 Ω (equal to r): I = 6 A, V = 6 V, load power 36 W — the maximum possible, since P(R) = ε^2 R/(R + r)^2 peaks at R = r — but efficiency has crashed to 50 per cent, and 36 W also burns inside the cell. Finally connect R = 11 Ω: current drops to 1 A, terminal voltage rises to 11 V, efficiency climbs to about 92 per cent, though the delivered power falls to 11 W. Read the pattern once and the whole topic becomes a graph in the head: terminal voltage rises toward ε, delivered power peaks at R = r, and efficiency climbs monotonically. ## Where the marks leak The distinction between emf and terminal voltage is the first leak: emf is measured by a potentiometer at null, while any voltmeter across the terminals reads V = ε - Ir, always a little low. The second leak is the maximum-power condition misapplied to efficiency: at R = r only half the generated power reaches the load, so power transmission deliberately runs far from R = r while signal matching (an amplifier to a speaker) sits exactly there. Third, the parallel-cells trap: identical cells in parallel do not multiply the current by n; they divide the internal resistance by n while emf stays put, and mixed groupings (m rows of n cells) give ε_eq = nε with r_eq = mr/n. Finally, a charging cell absorbs energy: V = ε + Ir means the terminal voltage exceeds the emf, and candidates who pattern-match the discharge formula contradict the stem's data. ## Frequently asked questions ### What is the difference between emf and terminal voltage? Emf is the energy supplied per coulomb by the cell's chemistry with no current flowing; terminal voltage V = ε - Ir is what the external circuit receives once the internal drop is paid — a potentiometer at null reads the former, any voltmeter the latter. ### When is the power delivered to a resistor maximum? When the external resistance equals the internal resistance, R = r, giving P_max = ε^2/4r at 50 per cent efficiency. ### Why does a voltmeter slightly under-read a cell's emf? The voltmeter draws a small current, so the terminal voltage falls below ε by the Ir drop — only a null method such as a potentiometer reads true emf. ### How do identical cells in series and in parallel differ? Series gives ε_eq = nε with r_eq = nr (higher voltage); parallel keeps ε_eq = ε but drops the internal resistance to r/n (steadier current, longer life). ### What happens if a cell is short-circuited? R = 0 limits the current to ε/r, large because r is small; all the power then dissipates inside the cell as heat.