For the system of four capacitors shown in Figure P 16.37, find (a) the total energy stored in t

step 1 In this question, we are given this circuit. We need to find a total energy stored in the system

For the system of four capacitors shown in Figure P 16.37,...

For the system of four capacitors shown in Figure $\mathrm{P} 16.37$, find (a) the total energy stored in the system and
(b) the energy stored by each capacitor. (c) Compare the sum of the answers in part (b) with your result to part (a) and explain your observation.

Key Concepts

Energy Storage in Capacitors

This concept relies on the well-known formula E = 1/2 * C * V^2, which quantifies the amount of energy stored in a capacitor given its capacitance (C) and the voltage (V) across it. It is a foundational idea in electromagnetism and circuit theory that is used to analyze energy storage on both a single capacitor level and within more complex networks.

Equivalent Capacitance in Networks

When capacitors are interconnected in series or parallel arrangements, their overall effect can be simplified by calculating an equivalent capacitance. This approach is essential in circuit analysis as it allows a complex network of capacitors to be represented as a single capacitor, making it easier to determine the overall energy storage and study the system’s behavior under applied voltages.

Series and Parallel Combinations

The organization of capacitors in series or parallel drastically affects both the voltage distribution and the charge on each capacitor. Recognizing how series circuits cause voltage drops to divide among capacitors while parallel circuits maintain the same voltage across each component is critical for accurate energy calculations in circuits, as these configurations shape the effective capacitance and energy distribution.

Energy Distribution in Capacitor Networks

Even though the overall energy stored in the network can be calculated using the equivalent capacitance, the energy on each individual capacitor is determined by its specific voltage and the local charge distribution. Comparing the sum of the individually computed energies to the energy computed from the equivalent capacitance can reveal differences that are important for understanding energy partitioning and the nuances of energy conservation within a network.

Transcript

00:01 In this question, we are given this circuit.

00:03 We need to find a total energy stored in the system, energy stored by each capacitor, and compare the sum of answers to the result in part a.

00:13 So to do this question, so i'm going to call this, i'm going to assign c1 is 3 micro -farrant, c -2 is 6 micro -faird, c -3 is 2 micro -faird, c4, c4, c4, 4 is 4 micro ferret.

00:40 And then c1 and c2 are in series.

00:47 So we can calculate c12 to be 1 over c1 plus 1 over c2 and take the reciprocal.

00:55 So we have 1 over 3 micro ferret plus 1 over 6 micro ferret and take the reciprocal.

01:03 We get 2 microferret.

01:08 And then for c34, we have 1 over c3 plus 1 over c4 and reciprocal.

01:19 So we have 1 over 2 microferret plus 1 over 4 microferret and we get 4 over 3 microferret.

01:30 So the effective capacitance, the equivalent capacitance will be c12 plus c34 because c12 and c34 are in parallel.

01:43 So we have 2 micro ferret plus 4 over 3 micro ferret.

01:51 Okay, we have 10 over 3 micro ferret.

01:54 Okay, so the total energy stored using u equals to half cb square.

02:02 Right, so u is half times 10 over 3 times 10 to pound negative 6 times 90 square and the answer is 0 .0135, three five juice.

02:17 Okay, so this is the answer for part a.

02:20 Next, i want to calculate the energy stored in each capacitor.

02:26 So we look at the circuit again.

02:37 So three micro ferret, six micro ferret, two micro ferret, four microferret.

02:45 Okay, so we know that the potential difference is 90 volts total...

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