In Fig. 25-18, C1=10.0 μF, C2=5.0 μF, and C3=4.0 μF . What is the change in their equivalent c

In Fig. 25-18, C1=10.0 μF, C2=5.0 μF, and C3=4.0 μF . What...

In Fig. $25-18, \quad C_{1}=10.0 \mu \mathrm{F}$, $C_{2}=5.0 \mu \mathrm{F}$, and $C_{3}=4.0 \mu \mathrm{F} .$ What is the change in their equivalent capacitance if (a) capacitors 1 and 2 are interchanged and (separately) (b) capacitors 1 and 3 are interchanged?

Key Concepts

Series and Parallel Combinations

This concept involves understanding how capacitors add their effects together when connected in series or in parallel. In a series combination, the equivalent capacitance is lower than any individual component and is calculated using the reciprocal formula, while in a parallel combination, the equivalent capacitance is the sum of all individual capacitors. This concept is critical for analyzing how the configuration of capacitors affects overall circuit behavior.

Equivalent Capacitance

Equivalent capacitance is the single capacitance value that can replace a network of capacitors without altering the overall charge storage capacity or voltage characteristics of the circuit. Calculating equivalent capacitance simplifies complex circuits and is fundamental in circuit analysis and design.

Effect of Component Interchange

In circuit analysis, the interchange of components refers to swapping the positions of elements within the circuit. Understanding the effect of such interchanges on the equivalent capacitance is important, as it tests the invariance of the circuit's overall properties when the circuit topology or configuration changes. This concept helps in verifying that only the connections and not the physical positions of the components ultimately determine the circuit behavior.

Transcript

00:01 In this question, we have been given a combination of three capacitors, out of which two of them are in parallel with each other.

00:08 So it's c1 and c2 are in parallel with each other.

00:13 And the entire combination of c1 and c2, they both are in series with c3.

00:20 So if i label it down, this one is c2, this is c1 and this is c3, and this is the battery or the voltage potential difference.

00:30 That is being applied.

00:32 So here we have been given the values of c1 as 10 mu f.

00:38 The value of c2 has been given as 5 mu f and the value of c3 is given to us as 4 microferrets.

00:47 Now we have to find out two things in this question.

00:51 So the two quantities that we're asked to find out is first that how will the capacitance equivalent capacitance of this combination changes c1 and c2 are interchanged.

01:03 So let us look at the first case here.

01:05 So firstly, we have to find out the equivalent t's c equivalent here in the original case.

01:11 So when c1 and c2 are at their place, so c original.

01:15 Now we first need to know the equivalent capacitance of this part of the circuit.

01:22 So here this one will be, you can say c0 will be c1 plus c2 because this is what is the formula for parallel capacitors and c1 and c2 then both of the addition will give us 15 mu f.

01:36 So this is c0.

01:37 Now c equivalent, we'll find out.

01:40 So this entire thing is in series with c3.

01:45 So direct formula will be c0 into c3 upon c0 plus c3.

01:52 This is for series combination.

01:54 So here we can put in the values...

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