Find equivalent capacitance
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Capacitors and Capacitance:
Capacitors make many electrical circuits work. To find the total capacitance of a circuit, you need the sum of each capacitor in it. This is done by adding whole numbers and fractions. The exact method depends on whether it is a series or parallel circuit.
Answer and Explanation:
A network can have one of two kinds of circuits. In parallel circuits, the wires with their components run next to each other. To find its total capacitance, you add the value of each capacitor. In a series circuit, the wire and its components are in a straight line. In this case, you add the inverse of each capacitance. Using these methods makes it easy to find the total capacitance of any network.
A capacitor, C, holds an electric charge, Q, across two plates. Its capacitance, C, equals the charge it has divided by the voltage, V, between the plates, or C = Q/V.
When capacitors are in parallel, the current will go by different paths. But this circuit had only one total voltage drop and one total charge. In effect, the individual capacitors can be viewed as being a single, bigger one. So to find the total capacitance, all that is needed is to add each capacitor, or:
C Total = C1 + C2 +…+ Cn.
For example, three capacitors are in parallel, with 10, 20, and 40 microfarads. This would be the same as one capacitor of 70 µF.
When doing this calculation, you must be sure the units for all the capacitors are the same! If some are in pF and others in µF you have to convert one set of units to the other. Otherwise, you will be adding numbers that have a 1000 times difference.
When capacitors are in series, the same current goes through all of them, so each has the same charge. So while C = Q/V still works and Q is the same for all the capacitors, each one its V will be only a fraction of the whole. This gives the following formula for total capacitance:
1/C Total = 1/C1 + 1/C2 +…+ 1/Cn.
To solve such an equation it is necessary to have a common denominator for the fractions.
For example, to find the total capacitance of the same capacitors that were given for the parallel circuit of 10, 20, and 40 µF, you would calculate them like this:
1/10 + 1/20 + 1/40 = 1/C. Using 40 as the common denominator for the fractions, we now have: 4/40 + 2/40 + 1/40 = 7/40.
Because the equation gives its answer as 1/C we and want to find the total capacitance, we must take the inverse of the final number. ''Flipping'' the fraction, we find that: C = 40/7, which is the same as 5.714 µF.
A handy check on your work is that in series circuits, total capacitance will always be less than that of the smallest capacitor.
If you have just two capacitors in series, you have a few tricks you can use to make this work easier. If the capacitors are equal, the total capacitance of the circuit is equal to half that of either one of them. So two capacitors in series each of 10 µF is the same as one of 5 µF.
If the capacitors are the same or different, you can find the answer by:
C Total = (C1 x C2) / (C1 + C2).
To use the last example, (10 x 10) / (10 + 10) = 100/20 = 5 µF.
In a complex circuit with both series and parallel components, the easiest way to calculate the total capacitance is to take each part separately and then add them together. For example, when several capacitors in series are along one branch of a parallel circuit, calculate their total C first. Then treat that number as though it was from a single capacitor in parallel with those on the other branches.
Note that the laws for capacitors in series and parallel are exactly the reverse of those for resistors.
Capacitors make many electrical circuits work. To find the total capacitance of a circuit, you need the sum of each capacitor in it. This is done by adding whole numbers and fractions. The exact method depends on whether it is a series or parallel circuit.
Answer and Explanation:
A network can have one of two kinds of circuits. In parallel circuits, the wires with their components run next to each other. To find its total capacitance, you add the value of each capacitor. In a series circuit, the wire and its components are in a straight line. In this case, you add the inverse of each capacitance. Using these methods makes it easy to find the total capacitance of any network.
A capacitor, C, holds an electric charge, Q, across two plates. Its capacitance, C, equals the charge it has divided by the voltage, V, between the plates, or C = Q/V.
When capacitors are in parallel, the current will go by different paths. But this circuit had only one total voltage drop and one total charge. In effect, the individual capacitors can be viewed as being a single, bigger one. So to find the total capacitance, all that is needed is to add each capacitor, or:
C Total = C1 + C2 +…+ Cn.
For example, three capacitors are in parallel, with 10, 20, and 40 microfarads. This would be the same as one capacitor of 70 µF.
When doing this calculation, you must be sure the units for all the capacitors are the same! If some are in pF and others in µF you have to convert one set of units to the other. Otherwise, you will be adding numbers that have a 1000 times difference.
When capacitors are in series, the same current goes through all of them, so each has the same charge. So while C = Q/V still works and Q is the same for all the capacitors, each one its V will be only a fraction of the whole. This gives the following formula for total capacitance:
1/C Total = 1/C1 + 1/C2 +…+ 1/Cn.
To solve such an equation it is necessary to have a common denominator for the fractions.
For example, to find the total capacitance of the same capacitors that were given for the parallel circuit of 10, 20, and 40 µF, you would calculate them like this:
1/10 + 1/20 + 1/40 = 1/C. Using 40 as the common denominator for the fractions, we now have: 4/40 + 2/40 + 1/40 = 7/40.
Because the equation gives its answer as 1/C we and want to find the total capacitance, we must take the inverse of the final number. ''Flipping'' the fraction, we find that: C = 40/7, which is the same as 5.714 µF.
A handy check on your work is that in series circuits, total capacitance will always be less than that of the smallest capacitor.
If you have just two capacitors in series, you have a few tricks you can use to make this work easier. If the capacitors are equal, the total capacitance of the circuit is equal to half that of either one of them. So two capacitors in series each of 10 µF is the same as one of 5 µF.
If the capacitors are the same or different, you can find the answer by:
C Total = (C1 x C2) / (C1 + C2).
To use the last example, (10 x 10) / (10 + 10) = 100/20 = 5 µF.
In a complex circuit with both series and parallel components, the easiest way to calculate the total capacitance is to take each part separately and then add them together. For example, when several capacitors in series are along one branch of a parallel circuit, calculate their total C first. Then treat that number as though it was from a single capacitor in parallel with those on the other branches.
Note that the laws for capacitors in series and parallel are exactly the reverse of those for resistors.
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