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Terminal Voltage Calculator

Enter EMF, current, internal resistance and charge/discharge mode to compute terminal voltage V=ε∓Ir, voltage drop Ir and internal power loss P=I²r. ε=12 V, I=2 A, r=0.5 Ω → discharge V=11 V, charge V=13 V.

Input Data

EMF ε (V). Lead-acid 12; Li-ion 3.7; dry cell 1.5; car battery 12.6.
V
Current I (A). Phone 0.5–3; car start 100–500; EV 50–300.
A
Internal resistance r (Ω). New lead-acid 0.01–0.1; old 0.5–1; Li-ion 0.05–0.2.
Ω
Discharge V=ε−Ir (smaller); charge V=ε+Ir (larger).

Results

Terminal voltage V (V).
12V
Internal resistance r (Ω). New lead-acid 0.01–0.1; old 0.5–1; Li-ion 0.05–0.2.
0Ω
Voltage drop across r (V).
0V
Power dissipated in r (W).
0W

At a glance:Terminal voltage V is the actual voltage measured at a battery or source's output terminals, distinct from its EMF ε. EMF (electromotive force) ε is the open-circuit voltage with no load; terminal voltage V is the real output, affected by internal resistance r: discharging V=ε−Ir (smaller than ε because r consumes voltage), charging V=ε+Ir (larger than ε because the external supply must overcome both r and ε). Internal power loss P=I²·r (Joule heat). History: Ohm summarised V=IR in 1827; Volta invented the voltaic pile in 1800, first observing internal-resistance effects. Classic example: a 12 V lead-acid cell with ε=12.6 V, r=0.5 Ω, discharging 2 A → V=12.6−1=11.6 V; a car starting at 200 A → V=12.6−100=negative (in reality polarisation lowers ε, but the drop is severe). Applications: (1) battery design — lower r improves performance; (2) power-supply analysis — output impedance matching; (3) solar panels — r affects conversion efficiency; (4) generators — armature resistance loss; (5) chargers — compute charge voltage.

Formula

Discharge: V = ε − I·r

Charge: V = ε + I·r

Internal loss: P = I²·r = V·I − ε·I

EMF: ε = V + I·r (discharge) or ε = V − I·r (charge)

Efficiency (discharge): η = V/ε = 1 − I·r/ε

$$V_{discharge} = \varepsilon - Ir, \quad V_{charge} = \varepsilon + Ir, \quad P_{loss} = I^2 r$$

How to Use

  1. Enter EMF ε (V), current I (A), internal resistance r (Ω) and the charge/discharge mode.
  2. The tool computes V=ε∓Ir (V), the drop Ir and internal loss P=I²r.
  3. Typical: 12 V battery ε=12, I=2, r=0.5 → discharge V=11 V, P=2 W; charge V=13 V.

Case Studies

Car battery and discharge

Lead-acid ε=12.6 V, r=0.5 Ω, discharge I=2 A → V=12.6−1=11.6 V.

Engine cranking at 200 A → V drops sharply; a weak battery can't start.

Charging needs V=ε+Ir above 12.6 V — the charger must overcome r.

Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.

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