Find current using KVL (with dependent source)

In summary, the conversation is about solving a circuit problem using Kirchoff's Voltage Law. The equations used are V = IR and the values for the resistors in the circuit are given. The mistake was made in accounting for the given detail that Ix is in mA. After correcting the error, the proper equations are a(6000) + (a-b)(2000) + 5x - 10=0, -5x + (b-a)(2000) + b(3000) + (b-c)(4000) = 0, 10 + (c-b)(4000) + c(2000) = 0, and x/1000 = -c.
  • #1
iharuyuki
16
1

Homework Statement


upload_2015-4-15_22-24-13.png


Homework Equations


V = IR
Kirchoff's Voltage Law

The Attempt at a Solution


[/B]
Top loop - a
Bottom right - b
Bottom left - c
Ix = x

KVL:
top: a(6000) + (a-b)(2000) + 5x - 10=0
bottom right: -5x + (b-a)(2000) + b(3000) + (b-c)(4000) = 0
bottom left : 10 + (c-b)(4000) + c(2000) = 0
x = -c

x comes out to 2 mA when it should be 1.5. Where did I make a mistake?

Thank you very much.
 
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  • #2
How did you account for the given detail that ##I_x## is in mA?
 
  • #3
got it! That was the error. The proper equations were this:

a(6000) + (a-b)(2000) + 5x - 10=0

-5x + (b-a)(2000) + b(3000) + (b-c)(4000) = 0

10 + (c-b)(4000) + c(2000) = 0

x/1000 = -c

Thank you very much!
 

Related to Find current using KVL (with dependent source)

1. What is KVL?

KVL stands for Kirchhoff's Voltage Law. It is a fundamental law in electrical circuit analysis that states that the sum of all voltages around a closed loop in a circuit must equal zero.

2. How do you use KVL to find the current in a circuit?

To use KVL to find the current in a circuit, you must first draw a closed loop around the circuit. Then, write an equation using KVL that sets the sum of all voltages around the loop equal to zero. Finally, solve the equation for the unknown current.

3. What is a dependent source?

A dependent source is a type of electrical component in a circuit whose output is controlled by an external input. It can be either voltage or current dependent, meaning its output depends on the voltage or current of another element in the circuit.

4. How do you handle dependent sources when using KVL?

When using KVL in a circuit with dependent sources, you must first choose a direction for the loop. Then, you can treat the dependent source as a regular voltage or current source, depending on its type. Use the dependent source's controlling variable in the KVL equation and solve for the current.

5. Can KVL be used in circuits with multiple loops?

Yes, KVL can be used in circuits with multiple loops. However, you must write a separate KVL equation for each loop and solve them simultaneously to find the unknown currents. It is important to choose the correct direction for each loop to ensure the equations are accurate.

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