What Voltage Should Be Applied to Achieve a Change in Capacitor Energy of 4uJ?

In summary, the conversation discusses a problem involving a circuit in the state of having an open switch. The goal is to calculate the voltage, E1, in order to achieve a change in the electrical energy of the capacitor of 4uJ. The attempt at a solution involves simplifying the circuit and using a superposition principle. The conversation also discusses the use of current divider and the concept of Thevenin's theorem in solving the problem. However, there are some discrepancies and uncertainties in the given solution, particularly with the placement of resistors and the use of Thevenin's theorem.
  • #1
diredragon
323
15

Homework Statement


This is the second problem from our test preparation cycle and i partially solved and understood it.
IMG_2330.JPG

The circuit in the picture is in the state of switch being open (STATE 1: SWITCH OPEN). Calculate ##E1## so that the change in the electrical energy of the capacitor is ##ΔW=4uJ##.

Homework Equations


3. The Attempt at a Solution [/B]
##ΔW=1/2ΔU^2_{1/2}C=4uJ##
##ΔU^2_{1/2}=\pm 2V## [there are two values and we can't determine which is correct so we work both]
##ΔU=ΔU_{ab}## [that voltage is the same for points A and B]
IMG_2331.JPG

Starting to simplify the circuit and added current generator to represent the change in that branch of the circuit:
##Δ=R1+R2+R3## [starting to transfer a triangle into a star]
##RA=\frac{R1R2}{Δ}##;##RB=\frac{R1R3}{Δ}##;##RC=\frac{R2R3}{Δ}## [finished with that]
##ΔU_{ab}=a*ΔIGK## [figured its a superposition principle where we find Uab if only IGK works]
##ΔIGK=\pm 2/55 mA## [immediate jump to the result, didnt quite get that, how did they get that? I am going to try to derive it myself] [dont get #1]
TRY:
##I_{branch}=ΔIGK*\frac{RB+R5}{RA+RB+R4+R5}## [tried the current divider to get the current in left part]
##U_{ab}=I_{branch}*(R4+RA)+ΔIGK*RC## [didnt check the results but i will, does this seem good though?]
Continuation of the solution:
IMG_2332.JPG

##ET=E\mp IR=\mp 2V## [so the theorem of compensation, putting the voltage source instead of the whole branch]
##I=ΔIGK## [the change that happens is that the current flows through the branch]
IMG_2333.JPG

##ET'=E1/8## [now this all of a sudden, how did they get to this?] [dont get #2]
##RT'=55## [the equivalent thevenin resistance i get this but the upper part i can't get still]
##ET'-ET+RT'I=0## [why +RT'I and not -RT'I?] [dont get #3]
##ET'=0 \Rightarrow E1=0##
##ET'0=4 \Rightarrow E1=32##
 
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  • #2
I'm not happy with your star resistance diagram in the second image.
If I label the left side of R2 as X and the right side of R3 as Y, for your equations to be right, RA connects to point A, RB connects to point Y, and RC connects to point X. The way you have drawn it suggests RA and RC swapped around.
 

FAQ: What Voltage Should Be Applied to Achieve a Change in Capacitor Energy of 4uJ?

What is a linear circuit?

A linear circuit is an electrical circuit in which the voltage and current have a linear relationship. This means that the output current is directly proportional to the input voltage.

How do you solve a linear circuit?

To solve a linear circuit, you can use a variety of techniques such as Kirchhoff's laws, Ohm's law, and the superposition theorem. These methods involve analyzing the circuit and using equations to calculate the voltage, current, and resistance at various points.

What are the key components of a linear circuit?

The key components of a linear circuit include resistors, capacitors, inductors, and voltage sources. These components are connected in a way that allows the circuit to function and produce a linear relationship between voltage and current.

What are some applications of solving linear circuits?

Solving linear circuits is essential in the design and analysis of electronic devices such as computers, smartphones, and household appliances. It is also used in industries such as telecommunications, power systems, and transportation.

What are some common challenges when solving linear circuits?

Some common challenges when solving linear circuits include complex circuit configurations, non-linear components, and the presence of noise. It is also important to ensure that all assumptions and approximations made during the analysis are valid to obtain accurate results.

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