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Electromotive Force

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Electromotive Force or EMF is the work done by the per unit charge while moving from the positive end to the negative end of the battery. It can also be defined as the energy gain per unit charge while moving from the positive end to the negative end of the battery.

The battery or the electric generator generates the electromotive force which causes the current to flow in the external circuit. These devices use another form of energy and convert them to electric energy.

Let’s learn more about Electromotive Force, its unit, and others in this article.

Electromotive Force Definition

Electromotive Force is defined as follows:

Electromotive Force is the electric potential generated by the battery or any electric source which allows the current flow to in the circuit. 

It is also called EMF which is the acronym for Electromotive Force. As the name suggests EMF is not any kind of force but rather it is the potential differences.

Any device which generates electric current has two terminals one positive terminal and one negative terminal. The work done by the unit charge in moving from the negative terminal of the battery to the positive terminal of the battery is defined as the Electromotive Force of the battery.

Electromotive Force Symbol 

Electromotive Force or EMF is represented using the Greek letter ε. It is the terminal potential difference of the circuit when no current flows in the circuit.

Electromotive Force Formula

Electromotive Force or EMF is calculated using the formula,

ε = V + Ir

where,
ε is the Electromotive Force
V is the Voltage of the Battery
I is the Current in the Circuit
r is the Internal Resistance of the Battery\

The above formula is used to calculate the EMF of the battery or cell. EMF of the cell is equal to the end potential difference of the cell when no current flows through the circuit.

Unit of EMF

As we know that EMF of the cell is the potential difference required to move a unit charge inside the circuit including the battery itself. Its SI unit is Voltage or Volt

It can also be expressed as Joule/Coloumb

Volts = Joule/Coulomb

Dimension of Electromotive Force

Dimension of Electromotive force is similar to the dimension of the potential difference. Its unit in the SI system is Joule/Coulomb thus its dimensional formula is  [M1L2T3I-1].

How do we calculate EMF?

We can easily determine the EMF of the cell or battery by measuring the voltage across the battery using the voltmeter.

The image showing the circuit diagram is given below,

Electromotive Force

 

Difference between Electromotive Force and Potential Difference

The basic difference between Electromotive Force and Potential Difference is discussed in the table below,

Electromotive Force

Potential Difference

The work done on a unit charge in the circuit is called the Electromotive Force.The energy required by the battery to move the charge in the circuit excluding the battery itself is called Potential difference.
EMF of any cell or battery is always constant.Potential difference of any circuit is not always constant it varies with the current in the circuit.
EMF of the circuit depends on the internal resistance of the circuit.Potential difference of the circuit does not depend on the internal resistance of the circuit.
EMF is represented using the Greek letter εPotential difference is represented using V.

Learn more about, Difference Between EMF and Voltage

Negative Electromotive Force

Electromotive Force of any battery can easily be negative when the battery charges i.e. in the case of charging the flow of the current in the circuit is opposite to the normal flow of the current.

Thus, the Electromotive Force is negative when the current flows in the opposite direction.

Difference between Terminal Voltage and EMF

There are various differences between Terminal Voltage and EMF and the major ones are discussed in the table below,

Terminal Voltage

EMF

The voltage difference at the end of the terminals of the battery in case of current flowing in the circuit is called the terminal voltage.The maximum voltage of the battery in case of no current flows is called the EMF of the battery.
It is represented by the letter V.It is represented by the Greek letter ε.
It is measured using the Voltmeter.It is measured using the Potentiometer.

Electromotive Force, Terminal Voltage, and Internal Resistance

When a battery is connected to a bulb, it lights it up. As more and more bulbs are connected to the battery, the intensity of the bulbs decreases. How does it happen? This happens because the output voltage of the battery is decreased. The reason for this can be attributed to two fundamental parts of a battery. A battery has two fundamental parts – electrical energy and internal resistance.  

Internal Resistance

It is known that a large emf-based battery has more size than the batteries with less emf. These batteries contain more energy and thus can deliver larger currents. Notice that a 12V battery of a truck can deliver more current than a 12V battery present in a motorcycle. The reason behind this can be attributed to the fact that the battery of the truck has less internal resistance than the battery of a motorcycle. 

Internal resistance is the inherent resistance that is present inside a voltage source. 

The figure below shows two fundamental parts of a voltage source. The emf present inside the battery and the resistance. This emf is denoted by ε while the internal resistance is denoted by ‘r’, both of them are series. The smaller the internal resistance for the battery, the more current it is able to supply to the circuit. The internal resistance of a battery can behave in complex ways, as the battery depletes the internal resistance of the battery increases. But it may also depend on the magnitude and the direction of the electric current through a voltage source, its temperature, and even the material the battery is made up of.

Terminal Voltage 

The voltage output of a battery is measured through its terminals and that is why it is called termed terminal voltage. In the figure given below, a battery and its internal resistance are shown. The battery is connected to another external resistance in series which is denoted by Rload. The net voltage developed across the terminals of the battery is given by the equation written below, 

Terminal Voltage

 

V = ε – Ir

where,
ε is the Electromotive Force
I is the Current flowing in the circuit
r is the internal resistance of the battery

I” is considered to be positive if the direction of its flow is from the negative to the positive terminal of the battery. The equation shows that the larger the current, the lower the terminal voltage of the battery. It can also be concluded that the smaller the internal resistance, the greater the terminal voltage. When the load resistor is taken into account, the current calculation becomes a little bit different. 

Equivalent Resistance of the circuit becomes, 

R = r + Rload

Current is given by Ohm’s law,

I = V/R = V/r + Rload

Read More,

Solved Examples on Electromotive Force

Example 1: Find the current that will flow inside the battery of 5 Volts and 0.02 ohms internal resistances in case its terminals are connected with each other. 

Solution: 

The current in that case will be given by simple application of ohm’s law. 

V = 5V 

r = 0.02 ohms. 

V = IR 

Plugging the values in the equation, 

I = V/R 

I = 5/0.02 

I = 250 A 

Example 2: Find the current that will flow inside the battery of 10 Volts and 2 ohms internal resistances in case its terminals are connected with each other. 

Solution: 

The current in that case will be given by simple application of ohm’s law. 

V = 10 V 

R = 2 ohms. 

V = IR 

Plugging the values in the equation, 

I = V/R 

I = 10/2 

I = 5 A 

Example 3: Find the current that will flow inside the battery of 20 Volts and 5 ohms internal resistances in case its terminals are connected with each other. Find the terminal voltage of the battery.  

Solution: 

The current in that case will be given by simple application of ohm’s law. 

V = 20 V 

R= 5 ohms. 

V = IR 

Plugging the values in the equation, 

I = V/R 

I = 20/5 

I = 4 A

The terminal voltage of the battery is given by, 

V = Emf – Ir

Given , emf = 20 V, I = 4A and r = 5

 V = Emf – Ir

V = 20 – (4)(5) 
V = 0 V 

Example 4: Find the current that will flow inside the battery of 20 Volts and 5 ohms internal resistances and 10 ohms load resistance in series. Find the terminal voltage of the battery.  

Solution: 

The current in that case will be given by simple application of ohm’s law. 

I = \frac{\text{emf}}{R_{\text{load}} + r}

Emf = 20 V 

Rload= 10 ohms. 

r = 5

plugging the values in the equation, 

I = \frac{\text{emf}}{R_{\text{load}} + r}

I = \frac{20}{10 + 5}

I = 1.33 A 

The terminal voltage of the battery is given by, 

V = Emf – Ir

Given , Emf = 20 V, I = 4/3 A and r = 5

 V = Emf – Ir

V = 20 – (1.33)(5) 

V = 20 – 6.65 

V = 13.35

Example 5: Find the current that will flow inside the battery of 10 Volts and 2 ohms internal resistances and 3 ohms load resistance in series. Find the terminal voltage of the battery.  

Solution: 

The current in that case will be given by simple application of ohm’s law. 

I = \frac{\text{emf}}{R_{\text{load}} + r}

Emf = 10 V 

Rload= 3 ohms

r = 2

Plugging the values in the equation, 

I = \frac{\text{emf}}{R_{\text{load}} + r}

I = \frac{10}{2 + 3}

I = 2 A 

Terminal voltage of the battery is given by, 

 V = Emf – Ir

Given , 

Emf = 10 V, I =2 A and r = 2

V = Emf – Ir

V = 10 – (2)(2) 

V = 10 – 6

V = 4V 

FAQs on Electromotive Force

Q1: What is Electromotive Force?

Answer:

The work done per unit charge in the complete cycle of the circuit is called the electromotive force.

Q2: How to find Electromotive Force?

Answer:

Electromotive force is calculated using the formula,

E = V + Ir

where
V is the potential difference
I is the current passing in the circuit
r is the internal resistance of the battery

Q3: What is Electromotive Force of a Cell?

Answer:

The electromotive force of the cell is defined as the terminal voltage of the cell when no current passes through it.

Q4: What is Dimension of Electromotive Force?

Answer:

The dimension of Electromotive force is [M1L2T-3I-1]

Q5: What is the unit of EMF?

Answer:

As we know electromotive force is the voltage thus, the SI unit for measuring the electromotive force is Volt.

Q6: What is the Potential Difference?

Answer:

The energy required by one unit charge form moving postive terminal of the battery to the negative termial of the battery is called the potential difference of the battery.

Q7: What is Terminal Voltage?

Answer:

The potential difference across the termials of the batery in the circuit is defined as the termianl voltage of the battery.



Last Updated : 04 Feb, 2024
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