A potentiometer wire of length L and a resistance r are connected in series with battery of e.m.f. E_o and a resistance r₁. An unknown e.m.f is balanced at a length l of the potentiometer wire. The e.m.f E will be given by

$fraction numerator LE subscript straight o straight r over denominator Ir subscript 1 end fraction$
$fraction numerator straight E subscript straight o straight r over denominator left parenthesis straight r space plus straight r subscript 1 right parenthesis end fraction. space I over L$
$fraction numerator straight E subscript straight o straight I over denominator straight L end fraction$
$fraction numerator LE subscript straight o straight r over denominator left parenthesis straight r plus straight r subscript 1 right parenthesis straight l end fraction$

Solution

fraction numerator straight E subscript straight o straight r over denominator left parenthesis straight r space plus straight r subscript 1 right parenthesis end fraction. space I over L

Consider a potentiometer wire of length L and resistance r are connected in series to a battery of emf E_o and a resistance r₁as shown in a figure.
Current in wire AB = E_o/r₁ +r

_{$Potential space gradient comma straight x space equals Ir over straight L space equals space open square brackets fraction numerator straight E subscript straight o over denominator straight r subscript 1 plus straight r end fraction close square brackets straight r over straight L emf space produced space across space straight E space will space be space given space by straight E space equals space straight x. straight l space equals space open square brackets fraction numerator straight E subscript straight o straight r over denominator straight r subscript 1 plus straight r end fraction close square brackets straight I over straight L$}

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

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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Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Current Electricity

A potentiometer wire of length L and a resistance r are connected in series with battery of e.m.f. Eo and a resistance r1. An unknown e.m.f is balanced at a length l of the potentiometer wire. The e.m.f E will be given by

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?