Concept explainers
Figure P27.75 shows four capacitors with CA = 4.00 μF, CB = 8.00 μF. CC = 6.00 μF. and CD = 5.00 μF connected across points a and b, which have potential difference ∆Vab = 12.0 V. a. What is the equivalent capacitance of the four capacitors? b. What is the charge on each of the four capacitors?
(a)
The equivalent capacitance of the four capacitors
Answer to Problem 75PQ
The equivalent capacitance of the four capacitors
Explanation of Solution
From figure 1,
Capacitors C and D are connected in series.
Write the expression for the equivalent capacitance CD in series.
Here,
The equivalent capacitance CD and B are connected in parallel.
Write the expression for the equivalent capacitance BCD in parallel.
Here,
The equivalent capacitance BCD and capacitor A are connected in series.
Write the expression for the equivalent capacitance ABCD in series.
Conclusion:
Substitute
Substitute
Substitute
Therefore, the equivalent capacitance of the four capacitors
(b)
Find the charge on each of the four capacitors
Answer to Problem 75PQ
The charge on each of the four capacitors are
Explanation of Solution
Write the expression for the charge on the equivalent capacitance.
Here,
From (IV),
Write the expression for the potential difference.
From (V), we can find the voltage across A and then the voltage across the BCD combination.
Here,
Conclusion:
The charge on A.
Substitute
Substitute
Substitute
The charge on B.
Substitute
The charge on C and D.
Here, C and D are in series, so the charge will be same. And the charge of B and C or D must sum to that on A.
Substitute
Therefore, the charge on each of the four capacitors are
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