(a)
The potential difference across the capacitor.
(a)
Answer to Problem 43P
The potential difference across the capacitor is
Explanation of Solution
Let the resistance across
When the circuit is connected with a voltage source, the capacitor starts to charge. So, it acts as an open circuit as shown in figure below.
Figure (1)
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
Write the expression to determine the potential difference
using the voltage division rule.
Write the expression to determine the potential difference across the capacitor.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the potential difference across the capacitor is
(b)
The time interval at which the capacitor discharges to one tenth of its initial voltage.
(b)
Answer to Problem 43P
The time interval at which the capacitor discharges to one tenth of its initial voltage is
Explanation of Solution
When the battery is disconnected, the capacitor starts discharging acting as a voltage source.
The circuit diagram is shown below after the battery is disconnected.
Figure (2)
The resistors
Write the expression for the equivalent resistance when the resistors are connected in series.
Here, the equivalent resistance is
Also, the resistors
Write the expression for the equivalent resistance when the resistors are connected in series.
Here, the equivalent resistance is
Now the resistors
Write the expression for the equivalent resistance when the resistors are connected in parallel.
Here, the equivalent resistance for the parallel connection is
Write the expression to calculate the time interval at which the capacitor discharges to one tenth of its initial voltage.
Here,
Substitute
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the time interval at which the capacitor discharge to one tenth of its initial voltage is
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Chapter 28 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
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