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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 = 1/3
- d)R = 2r
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two identical cells each of emf E and internal resistance r are connec...
According to max. power transfer theorem, power transferred to the load will be maximum when load resistance is equal to internal resistance
i.e., R = r/2
i.e., R = r/2
Most Upvoted Answer
Two identical cells each of emf E and internal resistance r are connec...
Solution:
Finding the expression for power developed across R:
Let V be the potential difference across R when the two cells are connected in parallel with the external resistance R. Then, using Kirchhoff's laws,
Potential difference across R, V = E - (ir) ...(1)
where i is the current flowing through each of the cells.
Using Ohm's law, we have
i = V/R
Substituting this expression for i in equation (1), we get
V = E - (V/R)r
Rearranging this expression, we get
V = (ER)/(R + r)
Substituting this expression for V in the expression for power developed across R, we get
P = V^2/R
Substituting the expression for V in this equation and simplifying, we get
P = [(E^2)R]/[(R + r)^2]
Finding the value of R for which P is maximum:
To find the value of R for which P is maximum, we differentiate the expression for P with respect to R and equate it to zero.
dP/dR = [E^2(r - R)]/[(R + r)^3] = 0
Solving for R, we get
R = r/2
Therefore, the value of R for which the power developed across it is maximum is R = r/2.
Finding the expression for power developed across R:
Let V be the potential difference across R when the two cells are connected in parallel with the external resistance R. Then, using Kirchhoff's laws,
Potential difference across R, V = E - (ir) ...(1)
where i is the current flowing through each of the cells.
Using Ohm's law, we have
i = V/R
Substituting this expression for i in equation (1), we get
V = E - (V/R)r
Rearranging this expression, we get
V = (ER)/(R + r)
Substituting this expression for V in the expression for power developed across R, we get
P = V^2/R
Substituting the expression for V in this equation and simplifying, we get
P = [(E^2)R]/[(R + r)^2]
Finding the value of R for which P is maximum:
To find the value of R for which P is maximum, we differentiate the expression for P with respect to R and equate it to zero.
dP/dR = [E^2(r - R)]/[(R + r)^3] = 0
Solving for R, we get
R = r/2
Therefore, the value of R for which the power developed across it is maximum is R = r/2.
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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 = 1/3d)R = 2rCorrect answer is option 'A'. Can you explain this answer?
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