Name: finding net capacitance in capacitor networks
Uploaded: 2023-09-18T17:11:16.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Physics

Energy

PHYS.PS3.13

Equivalent Capacitance

The net capacitance for a capacitor network can be calculated by finding the equivalent capacitances individually for the parallel only and series only combinations.
Consider a capacitor network consisting of a series and parallel combination of four capacitors connected to a battery. What is the charge across each capacitor?
Since capacitors 2 and 3 are connected in parallel, the sum of their capacitances gives the equivalent capacitance.
So, the four-capacitor network reduces to three capacitors connected in series.
Now, the charge on each capacitor has an equal magnitude, while the applied potential difference equals the sum of the voltage across each capacitor.
Since voltage equals the ratio of charge to capacitance, substituting the values of capacitances and applied voltage gives the charge accumulated on each capacitor in series.
The voltage across capacitors 2 and 3 are equal and can be obtained from the calculated charge.
Finally, the product of individual capacitances and voltage values gives the charges on capacitors 2 and 3.
So, the charges on all the capacitors in the network are estimated.

equivalent capacitance

Multiple capacitors can be connected in a circuit in series or parallel configuration. When the capacitor combination is connected to a battery, the potential drop across each capacitor and the magnitude of charge stored in the individual capacitor depends on the type of the connection. The capacitor combination is replaced by a single equivalent capacitor that stores the same amount of charge as the combination for a given potential difference.
The following strategies are adopted to calculate the net capacitance for a capacitor network:
<ol>
	<li>The capacitor network is grouped into capacitors connected in series and parallel in the network.</li>
	<li>A series combination&#39;s equivalent capacitor has the same charge magnitude as the individual capacitors. The potential difference across the series combination is the sum of potential differences across the individual capacitors. Finally, the sum of reciprocals of individual capacitances gives the reciprocal of the equivalent capacitance in a series circuit.</li>
	<li>The equivalent capacitor for a parallel combination has the same potential difference as the individual capacitor. The sum of the charges of the individual capacitors equals the charge of the equivalent capacitor. The equivalent capacitance equals the sum of all individual capacitances in the network.</li>
	<li>For series combinations, the magnitude of equivalent capacitance is smaller than any of the individual capacitances. On the contrary, the equivalent capacitance value is greater for the capacitors connected in parallel than any of the individual capacitances.</li>
	<li>All the series or parallel groups in the network are replaced with the equivalent capacitance in multiple steps till the net capacitance is obtained.</li>
</ol>

Multiple capacitors can be connected in a circuit in series or parallel configuration. When the capacitor combination is connected to a battery, the ...

Education

JoVE Core

Unit 1

Capacitance

KEY TERMS AND CONCEPTS

finding net capacitance in capacitor networks

Capacitor networks can be arranged in series or parallel, and the connection type changes how charge and voltage are shared. When the network is connected to a battery, the potential drop across each capacitor and the charge stored in each one depend on that arrangement. The full network can then be replaced by one equivalent capacitor that stores the same charge for the same potential difference.

To find the net capacitance, a capacitor network is grouped into series and parallel parts. A series combination has the same charge magnitude on each capacitor. The total potential difference across the series group is the sum of the individual potential differences, and the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances.

A parallel combination works differently. Each capacitor in parallel has the same potential difference. The total charge on the parallel group is the sum of the charges on the individual capacitors, and the equivalent capacitance is the sum of all the capacitances in that group.

These rules also show how the equivalent capacitance compares with the individual capacitors. For capacitors in series, the equivalent capacitance is smaller than any single capacitance in the group. For capacitors in parallel, the equivalent capacitance is greater than any single capacitance in the group.

Complex networks are solved in steps. Series or parallel groups are replaced by their equivalent capacitance, and the process is repeated until one net capacitance remains.

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Finding Net Capacitance in Capacitor Networks | JoVE K12

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Virginia  Standards of Learning

HIgh School

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PS.9

PS.9.a

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PHYS.PS3.15

Finding Net Capacitance in Capacitor Networks

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