For the system of capacitors shown in Fig. E24.16, find the equivalent capacitance (a) between b

For the system of capacitors shown in Fig. E24.16, find the...

Key Concepts

Capacitor Network Analysis

This is the process of systematically reducing a complex arrangement of capacitors into simpler series and parallel groups. By applying the rules for series and parallel combinations, one can determine the overall or equivalent capacitance between various nodes in the circuit. This analytical method is broadly applicable in both theoretical studies and practical design of electrical circuits.

Parallel Combination of Capacitors

Capacitors that are connected to the same two nodes are said to be in parallel. In parallel arrangements, each capacitor experiences the same voltage across its terminals, and the equivalent capacitance is simply the sum of the individual capacitances. This concept is essential for understanding how capacitors share the total stored charge in a network.

Equivalent Capacitance

This concept involves replacing a complex network of capacitors with a single capacitor that exhibits the same electrical behavior between two points. It is a fundamental simplification technique used in circuit analysis to ease the calculation of stored energy and charge distributions in the system.

Series Combination of Capacitors

When capacitors are connected end-to-end, they form a series combination. In such a configuration, the same charge passes through each capacitor, and the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances. This method is crucial for analyzing parts of a capacitor network where the components are linked in a single current path.

Transcript

00:01 So again we are given a combination of capacitors so let me draw the figure first so we have this first so let this point be this is a and we have this first capacitor let's call this c1 which is given to be 15 picofarad then we have another point here point b which is then connected to capacitors which are in parallel let's call this capacitor c2 which is given to be 9 microferred 9 picofared this is 9 picofarid and we have another capacitor here which is let's call this as c3 which is given to be 11 picofarid and there's a third point here which is c.

01:22 So this is the combination of capacitors which is given to us and in the first part of the problem we are being asked to find the equivalent capacitance between the points b and c so between these two points b and c we are required to find the equivalence capacitance so as we can see capacitors c2 and c3 are connected in parallel so so if i want to reduce this circuit, so i'm going to do like this.

02:00 So i have this capacitor c1, which is my 15 picofacet.

02:11 This is my point a.

02:16 I have another point b here.

02:20 And if i want to reduce the two capacitors, c2 and c3, which are connected in parallel, i'm going to write a new capacitor here.

02:27 Let's call this capacitor c prime, which is the equivalent capacitance of the two capacitor c2 and c3 and the third point c.

02:37 So since c2 and c3 are connected in parallel, so the equivalent capacitance is simply given by the sum of the two capacitors, c2 and c3.

02:51 So this is what happens for the parallel combination of capacitors.

02:57 So c2 is 9 microferred, 9 picof ferret plus c3 is 11 picomepoferred plus c3 is 11 which adds to 20 picofararad.

03:20 So this is the equivalent capacitance c prime between the point b and c so this is the first part of the problem part a...

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