07 Capacitors in Parallel and Series FINAL
CAPACITORS IN PARALLEL AND SERIES | CONCEPT OVERVIEW The topic of CAPACITORS IN PARALLEL AND SERIES can be referenced on page 201 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing. Capacitors, inductors, and resistors can all be present within the same circuit. Similar to resistors, capacitors and inductors can be combined together to calculate an equivalent capacitance or inductance. (See RESISTORS IN PARALLEL AND SERIES)
The equivalent capacitance for capacitors in PARALLEL is the sum of the capacitors in the circuit. This is calculated using this formula:
C P = C1 + C2 + C 3 + C 4 The formula for CAPACITORS IN PARALLEL can be referenced under the topic of CAPACITORS AND INDUCTORS IN SERIES AND PARALLEL on page 201 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing. 1|PREPINEER.COM
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Below is an example of capacitors that are in SERIES.
To calculate the equivalent capacitance of a circuit with capacitors in SERIES, we would use the formula:
CS =
1 1 1 1 1 + + + C1 C2 C 3 C 4
The formula for CAPACITORS IN SERIES can be referenced under the topic of CAPACITORS AND INDUCTORS IN SERIES AND PARALLEL on page 201 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing. If there are only 2 capacitors that are in SERIES, we can calculate the equivalent capacitance by using the formula for the PRODUCT-OVER-THE-SUM-RULE. This formula is helpful in saving time and reducing errors as it is concise and easy to follow.
CT=
C1 x C2 C1 +C2
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Where: • C 1 and C 2 are the capacitance values of the two capacitors in the circuit that are in series. It is important to remember that we can use this formula multiple times within a circuit to calculate multiple equivalences, as long as we are able to group 2 capacitors that are in series at a time. This formula will not work if we are trying to find the equivalent capacitance of more than 2 capacitors. If you are trying to calculate the equivalence of more than 2 capacitors, you must use the formula for capacitors in series from the Reference Handbook. We recommend using the product-over-the-sum-rule to double check your work, and make sure no errors were made or incorrect values used during your calculations. Note: This formula is not provided in the Reference Handbook.
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CONCEPT EXAMPLE: What is the equivalent capacitance for the circuit shown below?
SOLUTION: In this problem we are looking to calculate the equivalent or total capacitance of the circuit. Similar to calculating the equivalent resistance of a circuit, we will need to identify pairs or groups of capacitors that we can combine and simplify, until we are able to simplify the circuit to have one capacitor or total equivalent capacitance. There are many ways to approach this problem. The following depicts our recommended steps. We want to simplify the circuit. We will start with the group of 3 capacitors series that is on the right had side of the circuit. We will use the formula for capacitors in series to calculate the equivalent capacitance.
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CS =
1 1 1 1 + + C1 C2 C3
The formula for CAPACITORS IN SERIES can be referenced under the topic of CAPACITORS AND INDUCTORS IN SERIES AND PARALLEL on page 201 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing. Given capacitor values of 3 µF , 4 µF , and 9 µF , we calculate the first equivalent capacitance:
1 C EQ,1
=
1 1 1 + + 3 µF 4 µF 9 µF
C EQ,1 = 1.44 µF
Hint: Use the equation solve function on your calculator to avoid using the various algebra or fractional calculations in the equation. This is helpful for saving time and avoiding simple algebra errors. Next, we will use the calculated capacitance equivalence and the 7 µF capacitor to further simplify the circuit. These capacitors are in parallel, so we will use the following formula:
CP = C1 + C2 5|PREPINEER.COM
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The formula for CAPACITORS IN PARALLEL can be referenced under the topic of CAPACITORS AND INDUCTORS IN SERIES AND PARALLEL on page 201 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing. Plugging in our capacitor values, we can calculate the second equivalent capacitance using the formula for the equivalent capacitance of capacitors in parallel:
C EQ,2 = 1.44 µF + 7 µF = 8.44 µF Next, we will simplify the second capacitance equivalence we just calculated and the 1
µF capacitor that is in series with it. As there are 2 capacitors that are in series, we can calculate the third and total equivalent capacitance value of the circuit by using the PRODUCT-OVER-THE-SUMRULE.
CT=
C1 x C2 C1 +C2
Note: This formula is not provided in the Reference Handbook. Plugging in our capacitor values of 8.44 µF and 1 µF , we calculate the third and total equivalent capacitance of the circuit:
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CT=
1 µF x 8.44 µF 1 µF +8.44 µF
C T = 0.894 µF
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