For the capacitor network shown in Fig. P 24.55, the potential difference across a b is 12.0 V .

For the capacitor network shown in Fig. P 24.55, the...

Key Concepts

Voltage Distribution in Capacitor Networks

Understanding how voltage is distributed across capacitors in a network is crucial, particularly when they are arranged in series or mixed configurations. This concept helps in determining the potential difference across individual capacitors, which is necessary for calculating the energy stored in each component using the energy storage formula.

Capacitor Energy Storage

This concept involves understanding that the energy stored in a capacitor is given by the formula E = 1/2 CV², where C represents the capacitance and V is the voltage across the capacitor. This formula is essential for calculating how much energy a capacitor can store and is a cornerstone of analyzing energy in electrical circuits.

Equivalent Capacitance in Capacitor Networks

In complex circuits with multiple capacitors, it is often useful to replace the network with a single equivalent capacitor that has the same effect on the circuit. This process involves combining capacitances in series or parallel configurations to simplify calculations, particularly when determining the overall energy stored in the network.

Series and Parallel Capacitor Combinations

Capacitors can be connected in series or parallel, and each configuration affects the overall circuit behavior differently. In series combinations, the same charge appears on each capacitor while the total voltage is divided among them. In parallel combinations, all capacitors share the same voltage, while their individual capacitances add together to form the equivalent capacitance.

Transcript

00:01 In this question, we have this network, as can be seen from this figure, and we know that the potential difference between a and b is vab equals 12 .0 volts.

00:11 And we want to find the total energy stored in this entire system, and the energy stored in this particular capacitance.

00:21 And stored in this particular capacitor.

00:26 So the first thing we need to know is it's easiest if we start, finding the equivalent capacitors for this entire system okay so let's first start from these i will call this one two three four five just to make it easier to tell what i'm working on c three four so these are two in series so i will do this to get there it's six point two microferrant plus 1 over 11 .8 microferent.

01:11 And this gives us 4 .06 microferent.

01:17 And then we have this in parallel with c5 so c345 in total equals c34 plus c5 equals 4 .06 microferent plus 3 .50 microferent plus 3 .50 microferent equals 7 .56 microfarin.

01:49 Okay, so the last thing we need to do is we have this 345 as a whole in series with 1 and 2.

02:01 So the final c total equals 1 over c1 plus 1 over c2 plus 1 over c345 which is equal to 1 over 8.

02:15 Plus 1 over 4 .8 plus 1 over 7 .56.

02:25 And this gives us a total of this whole thing in terms of microfairant is 2 .19 microfariate.

02:36 Okay, so now we have the equivalent capacitance of this entire system.

02:42 And what is the total energy store? the energy stored is one half of cd square.

02:49 So one half times the total is 2 .19 times 10 to the negative 6 farrant times 12 .0 volts square, which is 4 .5x8 times 10 to the negative 4 jar, which is 158 microjab...

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