Enter the total emf (volts), the current (amps), and the resistance (ohms) into the calculator to determine the Terminal Voltage.
Terminal Voltage Formula
Terminal voltage is the actual voltage available at the terminals of a battery, cell, or source while current is flowing. In real sources, the terminal voltage is usually lower than the ideal EMF because some voltage is lost inside the source due to internal resistance.
V_t = E - I R
For a source delivering power to a load, this equation gives the usable output voltage seen at the terminals.
| Symbol | Description | Common Unit |
|---|---|---|
| Vt | Terminal voltage | volts (V) |
| E | Total EMF or ideal source voltage | volts (V) |
| I | Current supplied by the source | amps (A) |
| R | Internal resistance of the source | ohms (Ω) |
Rearranged Forms
Because the calculator can solve for any missing value, the terminal voltage equation is often rearranged as follows:
E = V_t + I R
I = \frac{E - V_t}{R}R = \frac{E - V_t}{I}How to Use the Calculator
- Enter any three known values.
- Select matching units for voltage, current, and resistance.
- Leave the unknown field blank.
- Calculate to find the missing variable.
Consistent units matter. If one value is entered in milliamps and another in ohms, the result will only be correct if the selected unit conversions match the entered values.
How to Interpret the Result
| Condition | What Happens to Terminal Voltage |
|---|---|
| No current flow | Terminal voltage matches the EMF because there is no internal voltage drop. |
| Higher current | Terminal voltage decreases because the internal drop becomes larger. |
| Higher internal resistance | Terminal voltage decreases more sharply under load. |
| Better source condition | Lower internal resistance helps the source maintain a voltage closer to its EMF. |
Example 1
A source has an EMF of 24 V, delivers 4 A, and has an internal resistance of 0.75 Ω.
V_t = 24 - 4(0.75)
V_t = 21 \text{ V}The source provides 21 V at its terminals while operating under load.
Example 2
A source has an EMF of 9 V, a terminal voltage of 8.4 V, and a current of 1.5 A. Find the internal resistance.
R = \frac{9 - 8.4}{1.5}R = 0.4 \ \Omega
This means the source loses 0.6 V internally at that operating current.
Common Mistakes
- Using load resistance instead of internal resistance.
- Mixing units such as mA, A, kΩ, and Ω without converting properly.
- Assuming terminal voltage is always the same as EMF.
- Ignoring the effect of increased current draw on source performance.
Where Terminal Voltage Matters
- Batteries: shows how much voltage is actually available when powering a device.
- Power supplies: helps evaluate voltage sag under load.
- Electrical testing: useful for estimating internal resistance and source health.
- Circuit design: helps ensure connected components receive the voltage they require.
In practice, terminal voltage is one of the clearest indicators of how a real source behaves under load. A large drop from EMF to terminal voltage usually points to high current demand, significant internal resistance, or both.
