Concept explainers
Referring to Fig. 25-13, what is the equivalent capacitance of the circuit across the 6.0-V battery? What are the voltages across
Fig. 25-13
The equivalent capacitanceacross the
Answer to Problem 66SP
Solution:
Explanation of Solution
Given data:
Refer to the circuit mentioned in the Fig.25-13.
The potential difference of the battery is
Formula used:
Write the expression for equivalent capacitance, when the capacitors are connected in series.
Here,
Write the expression for equivalent capacitance, when the capacitors are connected in parallel.
Write the expression for the charge on the capacitor.
Here,
Write the expression for the energy stored in the system of capacitors.
Here,
Explanation:
Consider the following figure 1.
From figure 1, the capacitors
Consider Figure 2, it is a reduced form of figure 1.
From figure 2, the capacitors
The expression for equivalent capacitance, when the capacitors are connected in parallel is,
Here,
Substitute
The resultant combination
The expression for equivalent capacitance, when the capacitors are connected in series is,
Here,
Substitute
Thus, the equivalent capacitance across the
Calculate the total charge flow in the circuit.
Write the expression for the charge on the capacitor.
Here,
Substitute
If the capacitors are connected in series, then the charge flow across each capacitor is same.
Thus, charge flow across the capacitor
Here,
The expression for the charge across thecapacitor
Here,
Substitute
Solve for
Since the capacitors
Here,
The capacitor
Here,
The charge across the parallel combination
The expression for the charge on the parallel combination
Substitute
Solve for
Since, the capacitors
The voltage across the capacitor
Here,
The expression for a charge on the capacitor
Here,
Substitute
Solve for
The
The expression for the energy stored in the capacitor
Substitute
Conclusion:
The equivalent capacitance across the
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Chapter 25 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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