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Cells, emf and internal resistances are interrelated concepts. A cell has both emf and internal resistance. An ideal cell is supposed to have zero internal resistance. Cells, emf and Internal resistance topic is part of Class 12 Physics Chapter 3 Current Electricity.
Cell: A cell is a device which provides necessary potential difference to an electric circuit to maintain continous flow of electric current in it.
EMF: Emf (Electromotive force) of a cell may be defined as the potential difference between the terminals of the cell when no current is drawn from it.
Internal resistance: Internal resistance of a cell is defined as the opposition offered by electrolytes and electrodes of a cell to the flow of electric current through it.
The formula for emf E is given by,
E = W/q
Where
- W = work done
- q = charge
The formula of internal resistance is given by,
E - V = Ir
Where
- E = emf
- V = Terminal potential or Voltage
- I = Current
- r = internal resistance
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Important Questions on Cells, emf, and Internal Resistance
Ques. Why does emf of a cell depend upon the concentration of electrolyte? (2 Marks)
Ans. Emf of a cell depends on the distance of electrodes, nature of the material of the electrodes and area of electrodes. It is inversely proportional to the concentration of electrolyte. Thus higher the concentration, lower the emf and vice versa.
Ques. Three identical cells, each of emf. 2v and unknown internal resistance are connected in parallel. This combination is connected to a 5ohm resistor. If the terminal voltage across the cell is 1.5volt. What is the internal resistance of each cell .hence define internal resistance of cell? (3 Marks)
Ans. Given
- Emf = 2v,
- Voltage =1.5v,
- Resistance = 5 ohms
r = 50 ohms
Ques. What is internal resistance? What are the factors that affect internal resistance? (2 Marks)
Ans. Internal resistance is the resistance offered by the cell due to the nature of the materials of the cell. The internal resistance is based on factors such as:
- Distance between electrodes
- Nature of electrode and electrolyte
- Area of electrode
Ques. A 5A current passes through an electric circuit for 6 minutes and 3600 J of work is done. Find the emf. (2 Marks)
Ans. Given
- Current = 5A
- Time = 6 minutes = 360 sec
- Work done = 3600J
We have,
Power = Work done/time
Power = 3600/360 = 10W
Power = emf x current
Therefore,
Emf = Power/ current
Emf = 10/5
Emf = 2V
Ques. A current passes through an electric circuit for 10 minutes and 1000 J of work is done. The emf is 20V. Find the current. (3 Marks)
Ans. Given
- Time = 10 minutes = 600 sec
- Work done = 1000J
We have
Power = Work done/time
Power =1000/600 = 5/3W
Power = emf x current
Therefore
Emf = Power/ current
20 = 5/3x I
I = 5/3 X20
I = 1/12
I = 0.8A
Ques. What is emf? (2 Marks)
Ans. Emf or Electromotive force is a force that is developed from the source which is used to drive the charges from one point to another. It is denoted by the symbol ε.
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Ques. The emf of a battery is 10v, current of 5A and internal resistance is 2 ohm. If the cell is connected to a resistor, find the resistance. (2 Marks)
Ans: Given
- emf = 10v
- Current = 5A
- Internal resistance = 2 ohm
We know that,
I = e/R + r
5 = 10/ R + 2
3/10 = 1/R
R = 3.3 ohms
Ques. The emf of a battery is 5v, current of 5A and internal resistance is 5 ohm. If the cell is connected to a resistor, find the resistance. (2 Marks)
Ans. Given
- emf = 10v
- Current = 5A
- Internal resistance = 2 ohm
We know that,
I = e/R + r
5 = 10/ R + 2
3/10 = 1/R
R = 3.3 ohms
Ques. A cell of emf E and internal resistance r is connected across an external resistance R. Plot a graph showing the variation of P.D. across R, versus R. (2 Marks)
Ans. The graph to show the variation of internal resistance r and external resistance R is given below.
Ques. The emf of a cell is always greater than its terminal voltage. Why? (2 Marks)
Ans. All cells have a definite amount of internal resistance due to the materials which it is made up of. Due to this, when current passes through a cell, there is a drop in potential across it due to its internal resistance. This is called the lost voltage. Thus the emf of a cell is greater than its terminal voltage.
Ques. Derive a relation between the internal resistance, emf and terminal potential difference of a cell from which current l is drawn. Draw V vs l graph for a cell and explain its significance. (5 Marks)
Ans. Consider the circuit shown.
By Kirchhoff’s rules we have
E – lR – rl = 0
E – V – lr = 0
E = V + lr
The V-l graph is as shown.
Significance of Graph: To find emf and internal resistance of the cell.
Ques. A voltmeter of resistance 998 ohms is connected across a cell of emf 2 V and internal resistance 2 Ohms. Find the potential difference across the voltmeter and also across the terminals of the cell. Estimate the percentage error in the reading of the voltmeter. (3 Marks)
Ans. Consider the following circuit diagram.
V= E – lr
998 × l = 2 – 2l
1000 l = 2
l = 0.002 A
Therefore,
V= 0.002 × 998= 1.996 V
Percentage error = (2-1.996)/2 x 100
= 0.004/2 = 0.2%
Ques. Gives the difference between Emf and the potential difference of a cell. (3 Marks)
Ans. The Difference between Emf and the potential difference of a cell is given below:
| Emf | Potential Difference |
|---|---|
| The difference of potential between two terminals of a cell when no current is drawn from it is called the Emf of a cell. | The difference of potential between two terminals of a cell when current is drawn from it is called the potential difference of a cell. |
| The emf of a cell is independent of the resistance of the external resistance. | The potential difference is directly proportional to the external resistance. |
| The emf of a cell is greater than the potential difference. | The potential difference is greater than the emf. |
| It is denoted by a symbol ε. | It is denoted by V. |
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