How to Calculate Terminal Voltage

In this piece, we’ll talk about how to calculate terminal voltage in an electrical circuit. You will also learn about EMF, the differences between EMF and terminal voltage and the step involved in calculating EMF in a circuit.

Use This Formula To Calculate Terminal Voltage

The general formula for calculating terminal voltage is:

Vterm = ϵ −Ir.

In this formula;

  • Vterm represents the existing voltage between the terminals of the battery (usually measured in volts, V)
  • ϵ represents the electromotive force (EMF) of the battery. This also refers to the total or maximum voltage (also measured in Volts, V)
  • I represent the total current flowing through the entire circuit (measured in amperes, A)
  • R represents the internal resistance existing within the battery (measured in Ohms, Ω)
  • Ir represents the voltage drops across the internal resistor. This can be rewritten as (V=IRV = IRV=IR).

Hence, we can adjust the whole formula as;

Vterm​= ϵ− Vr​

What is Terminal Voltage?

Terminal voltage is simply described as the measurement of the total voltage (the positive and the negative terminals) across the terminals of a battery where there is an absence of load connected to the terminal.

Usually, an ideal battery is a source of an electromotive force (EMF) that constantly maintains a terminal voltage, not dependent on the current flow between the two terminals. In an ideal battery, there is also an absence of internal resistance. Meanwhile, the terminal voltage equals the electromotive force of the battery.

Is Terminal Voltage the Same as EMF?

No! Terminal voltage is not the same as EMF.

The major difference between terminal voltage and EMF is that terminal voltage is small in comparison with EMF.

This implies that EMF has a much greater intensity than terminal voltage due to the existence of the voltage in a loaded circuit. As a result of the external forces, voltage drops or energy loss are often experienced, ultimately resulting in varying intensity. Meanwhile, EMF is always constant in terms of intensity.

Let’s take a look at other differences between terminal voltage and EMF;

Electromotive Force (EMF)
Terminal Voltage
1.EMF represents the voltage that is developed between the two terminals of a battery in the absence of electric current, i.e. both the positive and negative terminals of a battery.Terminal voltage represents the potential difference between the two electrode potentials of a battery regardless of the condition.
2.EMF is an open circuit voltageTerminal voltage is a closed-circuit voltage
3.EMF is dependent upon the internal resistance of the circuit, and it is also independent of the electrical circuit resistanceTerminal voltage, on the other hand, is directly proportional to the resistance between the positive and the negative terminals.
4.The formula for EMF is ε = I (R+r). In this equation, R represents the external resistance of the electrical circuit while r stands for the internal resistance of the given circuit.Terminal voltage is calculated with the formula; V = IR. In this case, I represents the current flowing through the circuit while the capital R stands for the external resistance of the electrical circuit.
5.The Electromotive Force of a circuit is usually measured with a potentiometer.In terminal voltage, it is measured with a Voltmeter.

EMF has a constant intensityTerminal voltage has varying intensity. This is a result of frequent drops across the external resistance.
6EMF is induced in a range of fields such as the electric, magnetic or gravitational fields.There is a restriction in the voltage inducement as it is only induced in an electric field.
7Work done in EMF represents the maximum work of the batteryWork done in terminal voltage doesn’t represent the maximum work of the cell or battery

How to Calculate Electromotive Force (EMF) in a Circuit

Electromotive Force (EMF) can be calculated with this formula;

ϵ = I (R + r)


ϵ = the symbol of electromotive force (EMF)

I = the current

R = the resistance of the circuit

Let’s say you have a circuit with a possible contrast of 3.2V and a current of 0.6A streaming plus the interior obstruction of the battery at 0.5 ohms. With this information, 

ϵ = I (R + r)

= 3.2 V + 0.6 A × 0.5 Ω

= 3.2 V + 0.3 V 

= 3.5 V

In summary, you’ve learned:

  • The definition of terminal voltage
  • How terminal voltage is calculated
  • The difference between EMF and Terminal Voltage and
  • The steps to calculate EMF in a circuit. 

With these, it is believed that you have improved your knowledge of terminal voltage and EMF in an electrical circuit. 

Ying Xu

Graduated from the University of Kansas with an Aerospace Engineering degree & served 4 years as an US Air Force officer. Experienced with basic survival skills, weapon system security,  technical disaster recovery, and system troubleshooting

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