(a)
The battery current just after closing switch S.
(a)
Answer to Problem 103P
The battery current just after closing the switch S is
Explanation of Solution
Given:
The value of emf is
The value of capacitances are
Formula used:
Apply Kirchhoff’s rule in circuit just after switch is closed,
Here,
Calculation:
Initially, the capacitor is uncharged so,
From equation (1), the battery current just after closing switch S is calculated as,
Conclusion:
Therefore, the battery current just after closing the switch S is
(b)
The battery current a long time after closing the switch S.
(b)
Answer to Problem 103P
The battery current a long time after closing the switch S is
Explanation of Solution
Formula used:
Apply Kirchhoff’s rule in circuit a long time after switch is closed,
Here,
Calculation:
From equation (2), the battery current a long time after closing switch S is calculated as,
Conclusion:
Therefore, the battery current a long time after closing the switch S is
(c)
The current in
(c)
Answer to Problem 103P
The current in
Explanation of Solution
Formula used:
Apply Kirchhoff’s rule at j unction of resistor
Apply Kirchhoff’s rule in loop 1,
Apply Kirchhoff’s rule in loop containing resistor
Calculation:
Differentiate equation (4) with respect to time,
Differentiate equation (5) with respect to time,
From equation (3) and (7),
From equation (4),
From equation (8) and (9),
Let the solution of above differential equation is,
Differentiate equation (10) with respect to time,
From equation (8) and (11),
Equate coefficient of
And,
At
From equation (10),
From equation (10),
Substitute values in equation (13),
Conclusion:
Therefore, the current in
(d)
The charges on capacitors plates a long time after reopening the switch S.
(d)
Answer to Problem 103P
The charges on capacitors plates a long time after reopening the switch S is zero.
Explanation of Solution
Calculation:
If the switch S is reopened, then after long time there will not be any flow of current in the circuit. Thus,
The potential difference across
The charges on
Conclusion:
Therefore, the charges on capacitors plates a long time after reopening the switch S is zero.
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Chapter 25 Solutions
Physics for Scientists and Engineers
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