A parallel combination of two cells of emfs E₁ and E₂ and internal resistance r₁ and r₂is used to supply current to a load of resistance R. Write the expression for the current through the load in terms of E₁, E₂, r₁ and r₂.

Solution

Given,
Emf of first cell = E₁
Emf of second cell = E₂
Internal resistances of two cell are r₁ and r₂ respectively.
Load resistance = R

Effective emf is given by, E_eff = $\frac{E_{1} r_{1} + E_{2} r_{2}}{r_{1} + r_{2}}$

Effective internal resistance, r_eff = $\frac{r_{1} r_{2}}{r_{1} + r_{2}}$

Now, the total resistance of the circuit would be the sum of load resistance and effective internal resistance.

R_total= R + r_eff = $R + \frac{r_{1} r_{2}}{r_{1} + r_{2}}$
Current through the load will be the same as the current through the circuit.
Thus,
$I = \frac{E_{eff}}{R_{total}}$ = $\frac{\frac{E_{1} r_{1} + E_{2} r_{2}}{r_{1} + r_{2}}}{R + \frac{r_{1} r_{2}}{r_{1} + r_{2}}}$ = $\frac{E_{1} r_{1} + E_{2} r_{2}}{R (r_{1} + r_{2}) + r_{1} r_{2}}$

which is the required expression for the current through the load.

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?

Answer the following questions:
Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.

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Current Electricity

A parallel combination of two cells of emfs E₁ and E₂ and internal resistance r₁ and r₂is used to supply current to a load of resistance R. Write the expression for the current through the load in terms of E₁, E₂, r₁ and r₂.

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?

Answer the following questions:
Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Current Electricity

A parallel combination of two cells of emfs E1 and E2 and internal resistance r1 and r2is used to supply current to a load of resistance R. Write the expression for the current through the load in terms of E1, E2, r1 and r2.

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?

Answer the following questions:Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A parallel combination of two cells of emfs E₁ and E₂ and internal resistance r₁ and r₂is used to supply current to a load of resistance R. Write the expression for the current through the load in terms of E₁, E₂, r₁ and r₂.

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?

Answer the following questions:
Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.