A potentiometer wire has a length of 10 m and resistance 4Ω. An accumulator of emf 2 V and a resistance box are connected in series with it. Calculate the resistance to be introduced in the box so as to get a potential gradient of 0.1 V/m

Solution

Given,
Length of the potentiometer wire, l= 10 m
Resistance of the potentiometer wire, R = 4Ω
Emf of the accumulator connected in series with the wire, E = 2V
A resistance box in series is connected to the potentiometer wire.
Resistance of the resistance box - ?

i) Required potential gradient, k = 0.1 V/m

Potential drop along the potentiometer wire, V=k.l
=0.1 $\times 10$ = 1 V

Therefore, current through the potentiometer wire,

I= $\frac{V}{R} = \frac{1}{4} = 0.25 A$
Let, R' be the resistace of the resistance box then,
Using the relation,
$I = \frac{E}{R + R'} 0.25 = \frac{2}{4 + R'} \Rightarrow 1 + 0.25 R' = 2 \Rightarrow 0.25 R' = 1 \Rightarrow R' = 4 Ω$

Thus, a resiatance of 4Ω has to be introduced in the resistance box.

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

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Current Electricity

A potentiometer wire has a length of 10 m and resistance 4Ω. An accumulator of emf 2 V and a resistance box are connected in series with it. Calculate the resistance to be introduced in the box so as to get a potential gradient of 0.1 V/m

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Current Electricity

A potentiometer wire has a length of 10 m and resistance 4Ω. An accumulator of emf 2 V and a resistance box are connected in series with it. Calculate the resistance to be introduced in the box so as to get a potential gradient of 0.1 V/m

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin? Current A Voltage V Current A Voltage V 0.2 0.4 0.6 0.8 1.0 2.0 3.94 7.87 11.8 15.7 19.7 39.4 3.0 4.0 5.0 6.0 7.0 8.0 59.2 78.8 98.6 118.5 138.2 158.0

Answer the following questions:A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?