Capacitance in series and parallel circuit

In summary, the problem involves finding the equivalent capacitance between nodes A and B for a group of capacitors. The 24 uF, 12 uF, and 8 uF capacitors are in series, while the 4 uF and 16 uF capacitors are in parallel. By combining the series and parallel combinations, the equivalent capacitance is found to be 1.678 micro farads.
  • #1
thatgirlyouknow
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[SOLVED] Capacitance in series and parallel circuit

Homework Statement



Determine the equivalent capacitance between A and B for the group of capacitors in the drawing.

Homework Equations



Cseries = 1/Cs = 1/c1 + 1/c2 + ...
Cparallel = Cp = C1 + C2 + ...

The Attempt at a Solution



The 4 and 12 micro farad capacitors are in parallel, so Cp = 16mf.
The other four are in series, so 1/5+1/24 = 1/C = 4.138mf (top)
1/6+1/8 = 1/C = 3.429mf (bottom)
All of these are in series, so 1/4.138+1/3.429+1/16 = 1/c; c = 1.678mf

This is not right. Where is my logic faulty?
 

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  • #2
The 24 uF, 12 uF and 8 uF capacitors are in series - since they are end to end between the two nodes in common with the 4 uF capacitor.

So find the capacitance of the series of 24 uF, 12 uF and 8 uF, and that combination is parallel with the 4 uF capacitor. That group is in series with the 5 uF and 6 uF capacitors between nodes A and B.
 
  • #3
thatgirlyouknow said:
The 4 and 12 micro farad capacitors are in parallel, so Cp = 16mf.
Capacitors are in parallel only if their ends are directly connected by nothing but a wire. That's not the case here, since the 24 and 8 micro farad capacitors are in the way.

Similarly, capacitors are in series only if there's nothing else in the path.

Do it step by step. Find the obvious combinations and replace them with their equivalents. Then redraw it, looking for more combinations.

The first combination that I see are several capacitors in series. Start there.
 
  • #4
Thanks guys; apparently I didn't quite understand how to combine initially. I get it now!
 

Related to Capacitance in series and parallel circuit

1. What is capacitance in a series circuit?

In a series circuit, capacitance refers to the total amount of stored electric charge that each capacitor in the circuit can hold. This value is determined by the capacitor's capacitance rating and the number of capacitors connected in series.

2. How is the total capacitance calculated in a series circuit?

The total capacitance in a series circuit is calculated by adding the reciprocals of each capacitor's capacitance values. In other words, it is equal to the inverse of the sum of the inverse values of each capacitor's capacitance. This can be represented mathematically as C(total) = 1/ (1/C1 + 1/C2 + 1/C3 + ...).

3. What happens to the total capacitance in a series circuit?

In a series circuit, the total capacitance is always less than the capacitance of the smallest capacitor in the circuit. This is because the capacitors are connected in a series, meaning that the same amount of charge passes through each capacitor. Therefore, the total capacitance is limited by the capacitor with the smallest capacitance.

4. What is capacitance in a parallel circuit?

In a parallel circuit, capacitance refers to the total amount of stored electric charge that each capacitor in the circuit can hold. Unlike a series circuit, the capacitors in a parallel circuit are connected side by side, meaning that the same voltage is applied to each capacitor.

5. How is the total capacitance calculated in a parallel circuit?

The total capacitance in a parallel circuit is equal to the sum of the capacitance values of each individual capacitor. This can be represented mathematically as C(total) = C1 + C2 + C3 + ... . This is because the voltage is the same across all capacitors in a parallel circuit, allowing for the total capacitance to be simply added together.

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