Terminal Voltage - Important Concept with Solved Examples

In essence, any electrical circuit consists of many components that we have known so far like resistance, inductor or a capacitor, and so forth. Among all the circuits we have seen, there are some important sources that play a very vital role in the operation and working of the circuit. Those are voltage and current sources. Let us discuss the voltage sources in detail. In some appliances, due to the depletion of the batteries inside them the energy produced by the appliance doesn't turn off completely. They start to show the level of energy decreased and this is because of the decline in the output voltage of the appliance. 

Say, we have a light and it starts dimming when the battery in it is depleted or overloaded. This is when we observe the decrease in the output voltage level. Every voltage source that we use in any circuit has an internal resistance along with energy sources. These are the reasons for the decline in the output voltage in depleted batteries. Let us dive into the concept of terminal voltage through the concept of what actually the voltage source and the internal resistance do in detail. 

Basic Parts of a Voltage Source 

As we have already discussed, there are two factors that affect the output voltage in a circuit. Those are the voltage source and the internal resistance. Let us start digging into these two things shortly.

Voltage Source: 

There are many voltage sources that play an essential role in electrical circuits. Many devices like mechanical generators, or motors could be able to run with some sort of energy from an energy source and many complex circuits can create voltage from natural resources like light and temperature. There is a capability for every device to create potential differences and be responsible for the working of the circuits. 

This happens when a small resistance is connected in series to the voltage source, then the source can be able to create the voltage potential difference which in turn is responsible for the passage of the current in the circuit. This is why this potential difference is described often as EMF. 

Electromotive Force or EMF: 

This stands for electromotive force and it is denoted by ɛ or E. This emf is something that would be created by non-electrical sources. For example, there are batteries that are non-electrical sources and they convert chemical energy into electrical energy when some connections are made with an energy source. This is when the Emf is produced. 

This emf is measured in volts as it is the difference between voltage potentials. EMF could be put in simpler terms like it is the potential difference across the voltage source when there is no current drawn from the device. Now, let us understand what internal resistance is.

Internal Resistance: 

In essence, any existing practical source which is considered a linear electric circuit can be assumed as a voltage source having an impedance in series with it. This is what we refer to as internal resistance. Generally, when there is no current flowing or drawn from the power source circuit, the total output voltage would surely be equal to the emf. But when the current starts flowing in the circuit, the output voltage measured or obtained will become less than the no-load voltage, i.e., emf. 

This is solely because of the internal resistance which causes the voltage drop across the resistor and contributes to the declination in the output voltage of the power source circuit. The internal resistance is represented by the letter 'r' and it is measured in ohms. 

The given figure below shows what any basic and a typical voltage source looks like. It is just an emf connected in series with internal resistance.

Emf with an internal resistance

Here, V is known as terminal voltage, and let's understand the concept of terminal potential difference and apprehend what is the terminal voltage of a cell.  

Terminal Voltage Formula 

Let us first dig into what is the terminal voltage of a cell. As the name describes, the terminal voltage is the voltage or potential difference between the positive and the negative terminals of the battery. It is denoted by the letter V and is measured in volts. If there is no energy drawn from the battery and no current is flowing in the circuit then the terminal voltage is equal to the emf. 

Eventually, the energy from the battery is used and it results in a decrease in the terminal voltage which becomes less than the emf. The terminal voltage formula is given by the equation, 

$V=\epsilon -Ir$ 

Here, Ir is the voltage drop across the internal resistance and e is the emf. 

Let us see how the internal resistance affects the current flowing in a circuit. Let us assume a cell of an end E is connected to a resistor R as shown in the circuit. 

Circuit with a voltage source and a resistance

As the cell would be having an internal resistance, that is r. Now we can apply Kirchhoff's law in the circuit, we get

$E - IR - Ir = 0$ 

$E = I(R+r)$ 

Therefore, $I=\dfrac{E}{R+r}$

In the above equation, if the value of r increases, then the current flowing in the circuit decreases. Let us look into an example problem of how to find terminal voltage. 

Solved Examples on Terminal Voltage

Example 1: In a circuit, the voltage at no load is given by 25V, and the internal resistance r = 3 ohms. If a current of 2A starts flowing in the circuit then find the terminal voltage across the source. 

Solution:

According to the terminal voltage equation, $V = E - Ir$ 

Given that, 

The voltage at no load, i.e., E = 25V 

Internal resistance, r = 3$\Omega$ 

Current, I = 2A 

Putting these values in the above equation, we obtain, 

V = 25 – 2(3) =  19V 

Therefore, the terminal voltage of the battery is 19V. 

Example 2: The terminal voltage across the terminals of the battery is 32V when the current flowing in the circuit is 6A. The internal resistance to the battery is 2 ohms. Find the emf of the battery cell.  

Solution:

Given that, the terminal voltage of the battery, V = 32V 

Current, I = 6A 

Internal resistance, r = 2Ω  

According to the terminal voltage equation, V = E - Ir 

Therefore, E = V + Ir = 32 + 6(2) = 44V 

Therefore, the emf of the battery is 44V.

Conclusion

Therefore, we have learned what is the terminal voltage of a cell and the evolution of the terminal voltage equation. The concept of the terminal potential difference is the basic source for all the important topics regarding electricity. We derived the terminal voltage formula and got a complete understanding of terminal potential difference through this article.