Concept explainers
Using Fig. 6.57, design a problem that will help other students better understand how capacitors work together when connected in series and in parallel.
Figure 6.57
Design a problem to make better understand how capacitors work together when connected in series and in parallel using Figure 6.57.
Explanation of Solution
Problem design:
For the circuit in Figure 6.57, determine the voltage across each capacitor and the energy stored in each capacitor.
Formula used:
Write the expression to calculate the energy stored in the capacitor.
Here,
Calculation:
Refer to Figure 6.57 in the textbook. The Figure 6.57 is redrawn as Figure 1 by assuming the voltage and capacitor values.
Refer to Figure 1, the capacitors
Write the expression to calculate the equivalent capacitance 1 for the series connected capacitors
Here,
Substitute
The reduced circuit of the Figure 1 is drawn as Figure 2.
Refer to Figure 2, the capacitors
Write the expression to calculate the equivalent capacitance 2 for the parallel connected capacitors
Here,
Substitute
The reduced circuit of the Figure 2 is drawn as Figure 3.
Write the expression to calculate the total applied voltage.
Here,
From the Figure 3, it is clear that the voltage across the capacitors with same capacitance value is equal. Therefore,
Substitute
Simplify the above equation to find
Therefore, from equation (5),
Write the expression to calculate the charge across the capacitor 1.
Here,
Substitute
Write the expression to calculate the charge across the capacitor 2.
Substitute
Refer to Figure 2, the capacitors
The combination of the series connected capacitors
Write the expression to calculate the voltage across the capacitor 3.
Substitute
Write the expression to calculate the voltage across the capacitor 4.
Substitute
Re-write the equation (1) to calculate the energy stored in capacitor
Substitute
Re-write the equation (1) to calculate the energy stored in capacitor
Substitute
Re-write the equation (1) to calculate the energy stored in capacitor
Substitute
Re-write the equation (1) to calculate the energy stored in capacitor
Substitute
Therefore, the value of the voltage across the capacitor 1
Conclusion:
Thus, the problem to make better understand how capacitors work together when connected in series and in parallel using Figure 6.57 is designed.
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