Circuit Analysis using KVL and KCL

In summary, the problem involves deriving an expression for the ratio (Vo/Vs) using KCL and KVL equations. The solution involves substituting values for Rs1, Rs2, and i and solving for Vp, which can then be used to calculate the ratio of (Vo/Vs). The key was recognizing that the 0.08Vp source is actually a current source, not a voltage source.
  • #1
syntha
2
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Homework Statement


Circuit_zps7dbcb83c.png


All variables are given by the circuit unless otherwise stated

a) Derive an expression for the ratio (Vo/Vs)

Homework Equations


KCL and KVL equations


The Attempt at a Solution



Rs1=2.55kΩ
-Vs+ .05Vo +(2.5kΩ/2.55kΩ)Vp = 0 where,

Vs = .05Vo + (2.5kΩ/2.55kΩ)Vp for the left circuit.

Then for the right circuit:

Rs2= 3.70kΩ where

.08Vp=iRs

i= .08Vp/3.70kΩ, so

Vo = iR
=(.08Vp/3.7kΩ)*20kΩ, solving for Vp gives me

Vp= Vo/.432 I then substituted this into my Vs equation and solved for (Vo/Vs) and was given a ratio of .432.

Now I am not sure if my approach to this problem is right but i think the logic in going this way seems right to me. Any help or criticism would be greatly appreciated.
 
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  • #2
The 0.08Vp source is a current source. So Vo = -0.08Vp*Rs2 ...(note the direction of current flow implied by the source).
 
  • #3
Yea I realized that its actually a current source and was able to solve the problem, my initial approach was totally off.
 

Related to Circuit Analysis using KVL and KCL

1. What is KVL and KCL in circuit analysis?

KVL (Kirchhoff's Voltage Law) states that the algebraic sum of voltages around a closed loop in a circuit must equal zero. KCL (Kirchhoff's Current Law) states that the algebraic sum of currents entering and leaving a node in a circuit must equal zero.

2. How do you apply KVL and KCL in circuit analysis?

To apply KVL, you must first select a closed loop in the circuit and assign a direction for current flow. Then, you can write an equation that sets the sum of all voltage drops equal to the sum of all voltage rises in the loop. To apply KCL, you must select a node in the circuit and write an equation that sets the sum of all currents entering the node equal to the sum of all currents leaving the node.

3. Why are KVL and KCL important in circuit analysis?

KVL and KCL are fundamental laws in circuit analysis that allow us to analyze and solve complex circuits. They provide a systematic way to determine the relationship between voltage, current, and resistance in a circuit and can be used to verify the accuracy of circuit calculations.

4. What are some common mistakes when using KVL and KCL in circuit analysis?

One common mistake is incorrectly labeling the direction of current flow in a closed loop for KVL. Another mistake is forgetting to include all currents at a node in KCL, leading to an incorrect equation. It is also important to use the correct sign convention for voltage drops and rises in KVL.

5. Can KVL and KCL be used in all circuits?

Yes, KVL and KCL can be used in all circuits, including both DC and AC circuits. However, they may not be the most efficient method for analyzing more complex circuits with multiple sources and varying components. In those cases, other circuit analysis techniques may be used in conjunction with KVL and KCL.

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