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Emf Of A Cell

Emf Of A Cell

Edited By Vishal kumar | Updated on Jul 02, 2025 05:52 PM IST

The electromotive force (EMF) of a cell is a fundamental concept in the study of electricity, particularly in understanding how cells and batteries power everyday devices. EMF represents the energy provided by a cell to move charges through a circuit, creating an electric current. Imagine the battery in your smartphone, which powers the device by converting chemical energy into electrical energy, enabling it to function. Just like the heart pumps blood to sustain life, the EMF acts as the driving force that pushes electrons through the circuit, ensuring that electrical appliances like fans, lights, and computers operate smoothly. Understanding the EMF of a cell is crucial not only for academic purposes but also for appreciating the underlying principles that govern the functioning of nearly all modern electronic devices. In this article, we will discuss the concept of Emf of A Cell. Electric current is the flow of electric charge through a conductor. This means that an electric current in a circuit is initiated by our continuous action or vibration of an atom as a result of force or the stimulus of another atom when contact is made with external conditions especially the source of Motive Force – Electromotive Force (EMF).

This Story also Contains
  1. What is a Cell?
  2. Electromotive Force (Emf) of a Cell
  3. Potential Difference
  4. Solved Examples Based on Cell and Emf of a Cell

What is a Cell?

A cell, in the context of electricity, is a device that converts chemical energy into electrical energy. It consists of two electrodes (an anode and a cathode) immersed in an electrolyte, a substance that conducts electricity. When the cell is connected to a circuit, a chemical reaction occurs between the electrodes and the electrolyte, which generates an electric current. This current flows through the circuit, powering electrical devices.

The Direction of Flow of Current

  1. inside the cell is from negative to positive electrode

  2. while outside the cell is from positive to negative electrode.

Electromotive Force (Emf) of a Cell

It is the work done / energy carried by a unit charge passing through one complete cycle of the circuit.

E=W/q

unit of emf is volt.

The EMF of a cell is also known as the potential difference across the terminals of a cell when it does not give any current.

Note- Cell is a source of constant emf but not constant current.

Potential Difference

It is the work done / energy carried by the unit charge passing through the external part (excluding the cell ) of the circuit.

The potential difference is equal to the product of the current and the resistance of that given part.

i.e. $V_{A B}=i R$.

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Solved Examples Based on Cell and Emf of a Cell

Example 1: In the circuit shown, current (in A) through the 50 V and 30 V batteries are, respectively

1) 2.5 and 3

2) 3.5 and 2

3) 4.5 and 1

4) 3 and 2.5

Solution:

KVL in loop abgha
$
\begin{aligned}
20 \mathrm{I}_1 & =50 \\
\mathrm{I}_1 & =2.5 \mathrm{~A}
\end{aligned}
$

KVL in loop abcdefgha
$
\begin{aligned}
& 50-5 I_2-30-5 I_2=0 \\
& I_2=2 \mathrm{~A}
\end{aligned}
$

KVL in loop cdefc
$
\begin{aligned}
& 30=10\left(\mathrm{I}_2+\mathrm{I}_3\right) \\
& \Rightarrow \mathrm{I}_2+\mathrm{I}_3=3 \\
& \mathrm{I}_3=3-2=1 \mathrm{~A}
\end{aligned}
$

therefore Current through 50 V battery is $=\mathrm{I}_1+\mathrm{I}_2=2.5+2.0=4.5 \mathrm{~A}$ current through 30 V battery $=\mathrm{I}_3=1 \mathrm{~A}$

Hence, the answer is the option (3).

Example 2:

In the above circuit value of R=10 r. If a total current of 1A is flowing through the circuit the value of E is?

1) 10 r
2) $11 r$
3) $9 r$
4) 0

Solution:

Electromotive force (Emf) of a cell

It is the work done / energy carried by a unit charge passing through one complete cycle of the circuit.

E=W/q

unit of emf is volt.

$\begin{aligned} & \frac{E}{10 r+r}=1 \\ & E=11 r\end{aligned}$

Hence, the answer is the option (2).

Example 3: A cell E1 of emf 6V and internal resistance $2 \Omega$ is connected with another cell E2 of emf 4V and internal resistance $8 \Omega$ ( as shown in the figure). The potential difference across points X and Y is:

1) 3.6V

2) 5.6V

3) 10.0 V

4) 2.0V

Solution:

The figure given in the question can be redrawn as given below

The direction of current in the circuit will be as shown in the figure.
So point Y is at a higher potential than X.
So $\mathrm{V}_{\mathrm{Y}}>\mathrm{V}_{\mathrm{X}}$
Current(I) in circuit,
$
\mathrm{I}=\frac{\mathrm{E}_1+\mathrm{E}_2}{\mathrm{r}_1+\mathrm{r}_2}=\frac{(6-4) \mathrm{V}}{(2+8) \Omega}=0.2 \mathrm{amp}
$

For positive potential $A$ is near to positive terminal of $E_2$ so has +4 V$
So potential across $\mathrm{E}_1$ and $\mathbf{E}_2$
$
\begin{aligned}
& \mathrm{E}_1=\mathrm{V}-\mathrm{Ir}_1=6-0.2 \times 2=6-0.4=5.6 \mathrm{~V} \\
& \mathrm{E}_2=\mathrm{V}+\mathrm{Ir}_2=4+0.2 \times 8=4+1.6=5.6 \mathrm{~V}
\end{aligned}
$

So potential between X and $\mathrm{Y}=E_2=5.6$ Volt.

Hence, the answer is the option (2).

Example 4:

In the above circuit value of R= 10 ohm and r= 1 ohm. If a total current of 1A is flowing through the circuit the potential drop (in V) across R is?

1) 10

2) 9

3) 11

4) 0

Solution:

Potential difference (V) It is the work done / energy carried by unit charge passing through the external part (excluding the cell ) of the circuit.

The potential difference is equal to the product of the current and the resistance of that given part.

i.e. $V_{A B}=i R$.
$
V=I R=10 \mathrm{~V}
$

Hence, the answer is the option (1).

Example 5: A voltmeter of resistance $1000 \Omega$ is connected across resistance $500 \Omega$ in a given circuit. What will be the reading of the voltmeter?

1) 4

2) 2

3) 6

4) 1

Solution:

$
\begin{aligned}
R_{e q} & =\frac{1000 * 500}{1500}+500 \\
& =500+\frac{1000}{3}=\frac{2500}{3} \Omega \\
I & =\frac{10}{\left(\frac{2500}{3}\right)} A=\frac{3}{250} A
\end{aligned}
$

Potential Difference across Voltmeter
$
\begin{aligned}
& \mathrm{V}=\mathbb{R} \\
& I_v=\left(\frac{3}{250}\right) \cdot \frac{R_2}{R_1+R_2}=\left(\frac{3}{250}\right) * \frac{500}{1500} \\
& I_v=\frac{1}{250} \mathrm{~A} \\
& \text { Potential Difference }=\frac{1}{250} * 1000 \mathrm{~V}=4 \mathrm{~V}
\end{aligned}
$

Summary

The EMF of a cell is the driving force that enables the flow of electric current in a circuit by converting chemical energy into electrical energy. The potential difference, which is the work done by a unit charge, depends on the current and resistance within the circuit. Understanding these concepts is key to solving problems related to electric circuits, such as determining current flow, potential differences, and the behaviour of batteries and resistors in various configurations.

Frequently Asked Questions (FAQs)

1. What is the EMF of a cell?
The EMF (electromotive force) of a cell is the maximum potential difference between its terminals when no current is flowing. It represents the energy per unit charge that the cell can provide to drive current through a circuit.
2. What factors affect a cell's EMF?
The EMF of a cell depends on the materials used for the electrodes and electrolyte, the concentration of the electrolyte, and the temperature. It does not depend on the size of the cell or the amount of current drawn.
3. How does temperature affect the EMF of a cell?
Temperature changes can affect the EMF of a cell by altering the rate of chemical reactions and the mobility of ions in the electrolyte. For most cells, EMF increases slightly with temperature, but the relationship is not always linear.
4. How does the EMF of a cell relate to its energy conversion?
The EMF of a cell represents the cell's ability to convert chemical energy into electrical energy. It indicates the maximum amount of energy per unit charge that the cell can provide to an external circuit.
5. Why doesn't the EMF of a cell depend on its size?
EMF is an intensive property that depends on the nature of the chemical reactions in the cell, not on the quantity of reactants. Increasing the size of a cell increases its capacity (total charge it can deliver) but not its EMF.
6. How does EMF differ from terminal voltage?
EMF is the maximum potential difference a cell can provide under ideal conditions (no current flow), while terminal voltage is the actual potential difference across the cell's terminals when current is flowing. Terminal voltage is always less than or equal to the EMF due to internal resistance.
7. Can the EMF of a cell be measured directly with a voltmeter?
No, a voltmeter cannot measure EMF directly. It measures the terminal voltage, which is close to the EMF when the current drawn is very small. To measure EMF accurately, special techniques like the potentiometer method are used.
8. How does the concept of EMF apply to renewable energy sources like solar cells?
In solar cells, EMF is generated by the photovoltaic effect rather than chemical reactions. The EMF represents the maximum potential difference that can be produced when the cell is illuminated, before any current is drawn.
9. Why does a cell's terminal voltage decrease when current flows?
When current flows, some voltage is lost due to the cell's internal resistance. This causes a voltage drop inside the cell, resulting in a lower terminal voltage compared to the EMF.
10. What is the significance of internal resistance in a cell?
Internal resistance represents the opposition to current flow within the cell itself. It affects the cell's performance by reducing the terminal voltage and limiting the maximum current the cell can provide.
11. How does the concept of EMF apply to biological systems?
In biological systems, EMF-like potentials exist across cell membranes and are crucial for processes like nerve signal transmission and ATP synthesis. These "bioelectric" potentials are generated by ion concentration gradients rather than redox reactions.
12. How does the EMF of a cell relate to its energy density?
While EMF doesn't directly determine energy density, it's a factor. Energy density depends on both the EMF and the total charge the cell can deliver. A higher EMF generally contributes to higher energy density, but other factors like electrode materials also play crucial roles.
13. What's the significance of EMF in the context of electroplating?
In electroplating, the EMF of the cell determines the direction and driving force of the plating process. The applied voltage must exceed the cell's EMF to drive the desired electroplating reaction in the forward direction.
14. How does the concentration of electrolyte affect a cell's EMF?
The concentration of the electrolyte can affect a cell's EMF through the Nernst equation. Generally, increasing the concentration difference between the two half-cells increases the EMF, but the relationship is logarithmic, not linear.
15. How does the EMF of a cell relate to its efficiency?
The EMF represents the maximum possible energy output per unit charge. The ratio of the actual useful energy output to this maximum (EMF multiplied by total charge) gives the cell's efficiency. Real cells always have efficiency less than 100% due to internal losses.
16. How does the concept of EMF apply to supercapacitors?
In supercapacitors, the equivalent of EMF is the maximum voltage that can be safely applied without breakdown of the dielectric. This voltage, like EMF in batteries, represents the energy storage capacity per unit charge.
17. How does the EMF of a cell relate to its self-discharge rate?
The EMF itself doesn't directly determine the self-discharge rate. However, cells with higher EMF may be more prone to side reactions that lead to self-discharge. The self-discharge rate is more directly related to the cell chemistry and construction.
18. What happens to the EMF of a cell as it discharges?
The EMF of a cell remains relatively constant during most of its discharge cycle. It only begins to decrease significantly when the cell is nearly depleted of its active materials.
19. Can a cell have zero internal resistance?
In practice, no cell can have zero internal resistance. All cells have some internal resistance due to the resistance of the electrolyte and electrodes. An ideal cell with zero internal resistance is a theoretical concept used in circuit analysis.
20. How does the EMF of a cell relate to its open-circuit voltage?
The open-circuit voltage of a cell is equal to its EMF. This is because when no current is flowing (open circuit), there is no voltage drop due to internal resistance, so the full EMF appears across the terminals.
21. Why is the EMF of a cell sometimes called its "ideal voltage"?
The EMF is called the "ideal voltage" because it represents the maximum potential difference the cell can provide under ideal conditions (no current flow, no internal losses). In real-world applications, the usable voltage is always less than this ideal value.
22. How does the EMF of a cell compare to the energy of the chemical reactions inside it?
The EMF of a cell is directly related to the free energy change of the chemical reactions occurring inside it. Specifically, the EMF multiplied by the charge transferred in the reaction equals the change in Gibbs free energy of the reaction.
23. Can the EMF of a cell be negative?
Yes, the EMF of a cell can be negative. This occurs when the cell is being charged (in rechargeable batteries) or when it's connected in reverse polarity in a circuit. The negative EMF indicates that energy is being put into the cell rather than extracted from it.
24. How does the concept of EMF apply to batteries with multiple cells?
In a battery with multiple cells connected in series, the total EMF is the sum of the individual cell EMFs. For cells in parallel, the EMF remains the same as that of a single cell, but the current capacity increases.
25. What's the relationship between a cell's EMF and its standard reduction potentials?
The EMF of a cell is equal to the difference between the standard reduction potentials of its cathode and anode. This relationship is key to predicting the EMF of different cell combinations using a table of standard reduction potentials.
26. Why doesn't increasing the surface area of electrodes increase a cell's EMF?
Increasing the surface area of electrodes doesn't change the EMF because EMF depends on the nature of the chemical reactions, not the reaction rate. However, larger surface area can reduce internal resistance and allow for higher current flow.
27. How does the EMF of a cell relate to its ability to do work?
The EMF of a cell represents its maximum ability to do electrical work per unit charge. It's a measure of the cell's potential to drive current through a circuit and power electrical devices.
28. Can the EMF of a cell exceed the theoretical maximum based on its chemical components?
No, the EMF of a cell cannot exceed the theoretical maximum determined by the free energy change of its chemical reactions. Any apparent excess would violate the laws of thermodynamics.
29. How does the concept of EMF apply to fuel cells?
In fuel cells, the EMF represents the maximum potential difference generated by the electrochemical reactions between the fuel and oxidizer. Like other cells, the actual voltage output is less than the EMF due to various losses.
30. What's the difference between EMF and potential difference in a circuit?
EMF is a property of the source (cell or battery) and represents its ability to drive current. Potential difference is measured between two points in a circuit and can vary depending on the circuit components and current flow.
31. Can the EMF of a cell change over time?
The EMF of a cell can change slightly over time due to factors like temperature fluctuations or gradual changes in the chemical composition of the electrodes or electrolyte. However, significant changes usually indicate cell degradation or failure.
32. How does pressure affect the EMF of a cell?
For most cells, pressure has minimal effect on EMF. However, in cells where gases are involved in the reactions (like fuel cells), pressure can affect the EMF according to the Nernst equation, with higher pressures generally increasing the EMF.
33. What's the relationship between a cell's EMF and its short-circuit current?
The short-circuit current of a cell is determined by its EMF divided by its internal resistance. A higher EMF or lower internal resistance will result in a higher short-circuit current.
34. How does the concept of EMF apply to thermoelectric devices?
In thermoelectric devices, the EMF is generated by the Seebeck effect, where a temperature difference creates a potential difference. The EMF in this case is proportional to the temperature difference between the hot and cold junctions.
35. Can a cell have a higher terminal voltage than its EMF?
No, a cell cannot have a higher terminal voltage than its EMF under normal operating conditions. The terminal voltage is always less than or equal to the EMF due to internal voltage drops when current flows.
36. What's the significance of the standard EMF in electrochemistry?
The standard EMF, measured under standard conditions (1M concentrations, 1 atm pressure, 25°C), provides a reference point for comparing different electrochemical cells and predicting the direction of spontaneous reactions.
37. Can the EMF of a cell be increased by external means?
The intrinsic EMF of a cell, determined by its chemical components, cannot be increased externally. However, cells can be connected in series to increase the total EMF of the battery system.
38. How does the EMF of a cell relate to its reversibility?
The EMF of a cell is directly related to its reversibility. In a perfectly reversible cell, the EMF would remain constant during charge and discharge cycles. Real cells show some variation due to irreversible processes and internal changes.
39. What's the relationship between a cell's EMF and the maximum current it can provide?
While EMF doesn't directly limit the maximum current, it plays a role. The maximum current is determined by the EMF divided by the total resistance (internal + external). A higher EMF allows for potentially higher currents, but internal resistance is often the limiting factor.
40. Can a cell with higher EMF always deliver more power than one with lower EMF?
Not necessarily. While a higher EMF provides greater potential for power delivery, the actual power output also depends on the cell's internal resistance and the external load. A cell with lower EMF but also lower internal resistance might deliver more power in some situations.
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