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If a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R₁ and R₂, when connected separately one after the other, across the cell, then the internal resistance of the cell is
- a)(R₁ + R₂)
- b)(R₁ - R₂)/2
- c)√R₁ R₂/2
- d)√R₁ R₂
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If a cell of constant electromotive force produces the same amount of ...
(R + R)/2
d)(2R)/(R+R)
Answer:
c) (R + R)/2
Explanation:
Let the internal resistance of the cell be r.
When one resistance R is connected, the current flowing through it is I1 = E/(R+r).
The heat produced in time t is Q1 = I1^2Rt = E^2Rt/(R+r)^2.
When the other resistance R is connected, the current flowing through it is I2 = E/(R+r).
The heat produced in time t is Q2 = I2^2Rt = E^2Rt/(R+r)^2.
Since the amount of heat produced is the same in both cases, we have Q1 = Q2.
Therefore, E^2Rt/(R+r)^2 = E^2Rt/(R+r)^2.
Simplifying this, we get R = R.
Hence, the internal resistance of the cell is (R + R)/2.
d)(2R)/(R+R)
Answer:
c) (R + R)/2
Explanation:
Let the internal resistance of the cell be r.
When one resistance R is connected, the current flowing through it is I1 = E/(R+r).
The heat produced in time t is Q1 = I1^2Rt = E^2Rt/(R+r)^2.
When the other resistance R is connected, the current flowing through it is I2 = E/(R+r).
The heat produced in time t is Q2 = I2^2Rt = E^2Rt/(R+r)^2.
Since the amount of heat produced is the same in both cases, we have Q1 = Q2.
Therefore, E^2Rt/(R+r)^2 = E^2Rt/(R+r)^2.
Simplifying this, we get R = R.
Hence, the internal resistance of the cell is (R + R)/2.
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Community Answer
If a cell of constant electromotive force produces the same amount of ...
(R + R)/2
d)(2R)/(R + R)
e)None of the above
We can use the formula for heat produced in a resistor:
H = I^2Rt
where I is the current, R is the resistance, and t is the time. Since the cell has a constant electromotive force, the current will be the same in both cases. Let's call the current I.
When the first resistance R is connected, the heat produced is:
H1 = I^2Rt
When the second resistance R is connected, the heat produced is:
H2 = I^2Rt
Since the amount of heat produced is the same in both cases, we can set H1 equal to H2 and solve for the internal resistance of the cell.
I^2Rt = I^2Rt
Rt = R + r + R
where r is the internal resistance of the cell. We can simplify this equation:
2Rt = 2R + r*t
r = 2Rt - 2R/t
r = 2R - 2R/t
r = (2R)/(1/t)
r = (2R)t
We don't know the value of t, but we do know that it is the same in both cases. So, we can say that t cancels out and the internal resistance of the cell is:
r = 2R
Therefore, the answer is (e) None of the above.
d)(2R)/(R + R)
e)None of the above
We can use the formula for heat produced in a resistor:
H = I^2Rt
where I is the current, R is the resistance, and t is the time. Since the cell has a constant electromotive force, the current will be the same in both cases. Let's call the current I.
When the first resistance R is connected, the heat produced is:
H1 = I^2Rt
When the second resistance R is connected, the heat produced is:
H2 = I^2Rt
Since the amount of heat produced is the same in both cases, we can set H1 equal to H2 and solve for the internal resistance of the cell.
I^2Rt = I^2Rt
Rt = R + r + R
where r is the internal resistance of the cell. We can simplify this equation:
2Rt = 2R + r*t
r = 2Rt - 2R/t
r = 2R - 2R/t
r = (2R)/(1/t)
r = (2R)t
We don't know the value of t, but we do know that it is the same in both cases. So, we can say that t cancels out and the internal resistance of the cell is:
r = 2R
Therefore, the answer is (e) None of the above.
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If a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R and R, when connected separately one after the other, across the cell, then the internal resistance of the cell isa)(R + R)b)(R - R)/2c)√R R/2d)√R RCorrect answer is option 'D'. Can you explain this answer?
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