(a)
The equilibrium charge on the capacitor as a function of
(a)
Answer to Problem 70AP
The equilibrium charge on the capacitor as a function of
Explanation of Solution
Let the resistance across
The resistors
Write the expression for the equivalent resistance when the resistors are connected in series.
Here, the equivalent resistance is
Write the expression to current through the series connection.
Here,
Write the expression to determine the potential difference across
Here,
The resistors
Write the expression for the equivalent resistance when the resistors are connected in series.
Here, the equivalent resistance is
Write the expression to current through the series connection.
Here,
Write the expression to determine the potential difference across
Here,
Write the expression to determine the potential difference across the capacitor.
Here,
Write the expression to calculate the amount of charge stored in the capacitor.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the equilibrium charge on the capacitor as a function of
(b)
The charge when
(b)
Answer to Problem 70AP
The charge when
Explanation of Solution
Write the expression for the equilibrium charge on the capacitor as a function of
Conclusion:
Substitute
Therefore, the charge when
(c)
Whether the charge on the capacitor can be zero and the value of
(c)
Answer to Problem 70AP
Yes, the charge on the capacitor can be zero when the value of
Explanation of Solution
Write the expression for the equilibrium charge on the capacitor as a function of
Conclusion:
Yes, the charge on the capacitor can be zero.
Substitute
Solve further.
Therefore, yes, the charge on the capacitor can be zero when the value of
(d)
The maximum possible value of the magnitude of charge and the value of
(d)
Answer to Problem 70AP
The maximum possible value of the magnitude of charge is
Explanation of Solution
Write the expression for the equilibrium charge on the capacitor as a function of
It is clear from equation (XI) that the maximum charge can be achieved when the term containing
This can be achieved by substituting zero for
Conclusion:
Substitute
Therefore, The maximum possible value of magnitude of charge is
(e)
Whether it is experimentally meaningful to take
(e)
Answer to Problem 70AP
It is experimentally not meaningful to take
Explanation of Solution
Write the expression for the potential difference across
Conclusion:
Substitute
Thus, this infinite value of voltage across the resistor
Therefore, it is experimentally not meaningful to take
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Chapter 28 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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