Find the potential difference across each cell and the rate of energy dissipation in R?

Solution

Applying Kirchhoff's rule for loop ABCDA,
$12 = 4 (I_{1} + I_{2}) + 2 I_{1}$
$12 = 6 I_{1} + 4 I_{2}$ ...(i)

For loop DEFAD
$6 = 4 (I_{1} + I_{2}) + I_{2}$
   $6 = 4 I_{1} + 5 I_{2}$ ...(ii)

Eqs. (i) and (ii) can be written as
   $12 = 6 I_{1} + 4 I_{2}$
and $9 = 6 I_{1} + 7.5 I_{2}$

On solving the above equatuions, we get

   $3 = - 3.5 I_{2}$

   $I_{2} = - \frac{3}{3.5} A$

Putting the value I₂ in equation (i)
   $12 = 6 I_{1} - \frac{4 \times 3}{3.5}$
$\Rightarrow$    $12 \times 3.5 = 6 \times 3.5 I_{1} - 12$
$\Rightarrow$    $12 (4.5) = 210 I_{1}$

$I_{1} = \frac{12 \times 4.5}{21} A$

   $= \frac{180}{7} = 25.7 A$

$∴$ Current in R,    $I = 25.7 - \frac{3}{3.5}$

Rate of energy dissipation = 2R

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

Find the potential difference across each cell and the rate of energy dissipation in 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?

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

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For Daily Free Study Material Join wiredfaculty

Current Electricity

Find the potential difference across each cell and the rate of energy dissipation in 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?

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

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.