A resistance R is connected across a cell, of emf E_x and internal resistance r_x. A potentiometer now measures the p.d. between the terminals of the cell, as V, state the expression for V in terms of E, r_x and R.

Solution

We are given E, r_x and R in series.
The equivalent resistance of the circuit is given by
R_equiv = R + r_x
Current flowing through the circuit , I = $\frac{E}{R + r_{x}}$
Hence,
Voltage drop across R is given by ohm's law,

V=IR

= $\frac{E R}{R + r_{x}}$

$\Rightarrow V = \frac{E}{1 + \frac{r_{x}}{R}}$

which is the required relation.

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 resistance R is connected across a cell, of emf E_x and internal resistance r_x. A potentiometer now measures the p.d. between the terminals of the cell, as V, state the expression for V in terms of E, r_x and R.

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 resistance R is connected across a cell, of emf Ex and internal resistance rx. A potentiometer now measures the p.d. between the terminals of the cell, as V, state the expression for V in terms of E, rx and R.

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

A resistance R is connected across a cell, of emf E_x and internal resistance r_x. A potentiometer now measures the p.d. between the terminals of the cell, as V, state the expression for V in terms of E, r_x and R.

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?