(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 Technology Update
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- (a) Determine the equilibrium charge on the capacitor in the circuit of Figure P27.46 as a function of R. (b) Evaluate the charge when R = 10.0 . (c) Can the charge on the capacitor be zero? If so, for what value of R? (d) What is the maximum possible magnitude of the charge on the capacitor? For what value of R is it achieved? (c) Is it experimentally meaningful to take R = ? Explain your answer. If so, what charge magnitude does it imply? Figure P27.46arrow_forwardIf a capacitor, C=30.4 μF is suddenly connected to a circuit with the total resistance of R =10.22 Ὼ in the circuit with a battery of any capacity, how much time (in microseconds) will elapse for the voltage on the capacitor to be 60 % that of the battery?arrow_forwardA capacitor of capacitance C = 4.5 uF is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 8.5 kOhm, and a battery which provides a potential difference of VB = 105V. (a) Calculate the time constant t for the circuit in seconds. (b) After a very long time after the switch has been closed, what is the voltage drop VC across the capacitor in terms of VB? (c) Calculate the charge Q on the capacitor a very long time after the switch has been closed in C. (d) Calculate the current I a very long time after the switch has been closed in A. (e) Calculate the time t after which the current through the resistor in one-third of its maximum value in s. (f) Calculate the cahrge Q on the capacitor when the current in the resistor equals one third its maximum value in C.arrow_forward
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- A capacitor of capacitance C = 7.5 μF is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 11.5 kΩ, and a battery which provides a potential difference of VB = 110 V. (a) Calculate the time constant τ for the circuit in seconds. (b) After a very long time after the switch has been closed, what is the voltage drop VC across the capacitor in terms of VB? (c) Calculate the charge Q on the capacitor a very long time after the switch has been closed in C.arrow_forwardThe figure below shows how a bleeder resistor (R = 250 kΩ) is used to discharge a capacitor (C = 90.0 µF) after an electronic device is shut off, allowing a person to work on the electronics with less risk of shock. (a) What is the time constant? _______s (b) How long will it take to reduce the voltage on the capacitor to 0.100% of its full value once discharge begins? _______s (c) If the capacitor is charged to a voltage V0 through a 150 Ω resistance, calculate the time it takes to rise to 0.865V0 (this is about two time constants). _______sarrow_forwardA 1.0 μF capacitor is being charged by a 9.0 V battery through a 10 MΩ resistor. (A) Determine the potential across the capacitor at time t=1.0 s. Express your answer in volts. (B) Determine the potential across the capacitor at time t=5.0 s Express your answer in volts. (C) Determine the potential across the capacitor at time t=20 s. Express your answer in volts.arrow_forward
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