(a)
The time constant for the charging of capacitor.
(a)
Answer to Problem 115P
The time constant for the charging of capacitor is
Explanation of Solution
Given:
The given values in the circuit are,
And,
Formula Used:
The expression for the time constant for charging the capacitor is given by,
Calculation:
The time constant for charging the capacitor is calculated as,
Conclusion:
Therefore, the time constant for the charging of capacitor is
(b)
The proof that the potential across switch increases from
(b)
Answer to Problem 115P
The proof that as the potential across switch increases from
Explanation of Solution
Given:
The given values in the circuit are,
And,
Formula Used:
The expression for the voltage across the charging capacitor is given by,
Now,
Let ,
Rewrite equation (I) as,
Expand the term
Equation (II) can be written as,
This is a linear function.
Conclusion:
Therefore, the proof that as the potential across switch increases from
(c)
The changed value of
(c)
Answer to Problem 115P
The changed value of
Explanation of Solution
Given:
The given values in the circuit are,
And,
Formula Used:
The expression for the potential across the capacitor is given by
Calculation:
The changed value of
Conclusion:
Therefore, the changed value of
(d)
The time elapse during the discharge of capacitor when the switch
(d)
Answer to Problem 115P
The time elapse during the discharge of capacitor when the switch
Explanation of Solution
Given:
The given values in the circuit are,
And,
Formula Used:
The expression for the potential difference across the capacitor is given by,
The expression for
Rewrite equation (III) as,
Calculation:
The time elapsed during the discharge of capacitor is calculated as,
Conclusion:
Therefore, the time elapse during the discharge of capacitor when the switch
(e)
The average rate at which the energy is delivered to resistor
(e)
Answer to Problem 115P
The average rate at which the energy is delivered to resistor
Explanation of Solution
Given:
The given values in the circuit are,
And,
Formula Used:
The expression for the rate at which energy is dissipated in
The current varies with time. So, integrate over time.
The expression for the rate at which energy is dissipated in the switch resistance is given by,
Calculation:
The value of
The value of
The rate at which energy is dissipated in the switch resistance is calculated as,
Conclusion:
Therefore, the average rate at which the energy is delivered to resistor
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Chapter 25 Solutions
Physics for Scientists and Engineers
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