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8 identical cells, each of emf E and internal resistance r, are connected in series. If polarity of two cells is reversed, then the total internal resistance in the circuit will be
- a)8 r
- b)6 r
- c)4 r
- d)2 r
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
8 identical cells, each of emf E and internal resistance r, are connec...
- Resistance is the inherent property of a body and is independent of its alignment, so even if the polarity is reversed, the resistance will be same.
- Here, emf of each cell = E
Internal resistance of each cell = r - Total internal resistance of 8 cells connected in series is: rseries = 8r
- If the polarity of two cells are reversed, then the total internal resistance of the cells is: r′series = 8r
i.e., there is no effect on the total internal resistance of the cells.
Most Upvoted Answer
8 identical cells, each of emf E and internal resistance r, are connec...
Solution:
Given,
Number of cells, n = 8
EMF of each cell, E = constant
Internal resistance of each cell, r = constant
When all the cells are connected in series, the total emf of the circuit will be nE, and the total internal resistance will be nr.
Total emf of the circuit = 8E
Total internal resistance of the circuit = 8r
Now, if the polarity of two cells is reversed, the net emf of the circuit will not change, but the internal resistance of the circuit will decrease.
To find the new internal resistance of the circuit, we need to find the equivalent resistance of the two cells that have been reversed in polarity.
Let's say the two cells with reversed polarity are cells number m and n, where m < />
When cells m and n are reversed in polarity, the equivalent resistance of these two cells will be:
Req = (2r)/(1 - E^2/r^2)
Now, the equivalent resistance of the entire circuit, including the two reversed cells, can be calculated using the formula for series combination of resistors:
Req_total = nr + Req
Substituting the value of Req, we get:
Req_total = nr + (2r)/(1 - E^2/r^2)
Simplifying this expression, we get:
Req_total = (8r^3 - 2rE^2)/(r^2 - E^2)
Since r and E are constants, the new internal resistance of the circuit depends only on the number of cells and not on the values of r and E.
Therefore, the correct answer is option A, 8r.
Given,
Number of cells, n = 8
EMF of each cell, E = constant
Internal resistance of each cell, r = constant
When all the cells are connected in series, the total emf of the circuit will be nE, and the total internal resistance will be nr.
Total emf of the circuit = 8E
Total internal resistance of the circuit = 8r
Now, if the polarity of two cells is reversed, the net emf of the circuit will not change, but the internal resistance of the circuit will decrease.
To find the new internal resistance of the circuit, we need to find the equivalent resistance of the two cells that have been reversed in polarity.
Let's say the two cells with reversed polarity are cells number m and n, where m < />
When cells m and n are reversed in polarity, the equivalent resistance of these two cells will be:
Req = (2r)/(1 - E^2/r^2)
Now, the equivalent resistance of the entire circuit, including the two reversed cells, can be calculated using the formula for series combination of resistors:
Req_total = nr + Req
Substituting the value of Req, we get:
Req_total = nr + (2r)/(1 - E^2/r^2)
Simplifying this expression, we get:
Req_total = (8r^3 - 2rE^2)/(r^2 - E^2)
Since r and E are constants, the new internal resistance of the circuit depends only on the number of cells and not on the values of r and E.
Therefore, the correct answer is option A, 8r.
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Community Answer
8 identical cells, each of emf E and internal resistance r, are connec...
Resistance will always be added in series whether the polarity is same of cell or not...but emf of 2 cell cancels out so emf will be 6E and resistance 8r
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8 identical cells, each of emf E and internal resistance r, are connected in series. If polarity of two cells is reversed, then the total internal resistance in the circuit will bea)8 rb)6 rc)4 rd)2 rCorrect answer is option 'A'. Can you explain this answer?
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