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Two identical cells each of emf E and internal resistance r are connected in parallel with an external resistance R. To get maximum power developed across R, the value of R is
- a)R = r/2
- b)R = r
- c)R = r/3
- d)R = 2r
Correct answer is option 'A'. Can you explain this answer?
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Two identical cells each of emf E and internal resistance r are connec...
For max. power consumption. I should be max. So denominator should be min. for that
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Two identical cells each of emf E and internal resistance r are connec...
Solution:
The circuit diagram of the given problem is shown below.
Let the current flowing through each cell be I. Then, the total current flowing through the external resistance R is 2I.
The total emf of the two cells in parallel is E. The total internal resistance of the two cells in parallel is r/2.
Using Kirchhoff's loop rule in the outer loop, we get:
2I(R + r/2) = 2E
I(R + r/2) = E
I = E / (R + r/2)
The power developed across the external resistance R is given by:
P = I²R
Substituting the value of I, we get:
P = (E²R) / (R+r/2)²
To get the maximum power, we differentiate P w.r.t. R and equate it to zero.
dP/dR = (E²(R+r/2)² - 2E²R(R+r/2)) / (R+r/2)⁴
Equating dP/dR to zero, we get:
E²(R+r/2)² - 2E²R(R+r/2) = 0
(R+r/2)² = 2R(R+r/2)
(R+r/2) = 2R
R = r/2
Therefore, the value of R to get maximum power developed across it is R = r/2.
Hence, option A is the correct answer.
The circuit diagram of the given problem is shown below.
Let the current flowing through each cell be I. Then, the total current flowing through the external resistance R is 2I.
The total emf of the two cells in parallel is E. The total internal resistance of the two cells in parallel is r/2.
Using Kirchhoff's loop rule in the outer loop, we get:
2I(R + r/2) = 2E
I(R + r/2) = E
I = E / (R + r/2)
The power developed across the external resistance R is given by:
P = I²R
Substituting the value of I, we get:
P = (E²R) / (R+r/2)²
To get the maximum power, we differentiate P w.r.t. R and equate it to zero.
dP/dR = (E²(R+r/2)² - 2E²R(R+r/2)) / (R+r/2)⁴
Equating dP/dR to zero, we get:
E²(R+r/2)² - 2E²R(R+r/2) = 0
(R+r/2)² = 2R(R+r/2)
(R+r/2) = 2R
R = r/2
Therefore, the value of R to get maximum power developed across it is R = r/2.
Hence, option A is the correct answer.
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Two identical cells each of emf E and internal resistance r are connected in parallel with an external resistance R. To get maximum power developed across R, the value of R isa)R = r/2b)R = rc)R = r/3d)R = 2rCorrect answer is option 'A'. Can you explain this answer?
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