Kirchhoff's First Law to solve a circuit with 2 loops

In summary, the conversation discusses Kirchhoff's laws and calculations involving potential drops and currents in a circuit. The method and results are deemed correct and a question about the direction of the circuit is clarified. The equation -12V -125I3 +75I2=0 is confirmed to equal zero due to Kirchhoff's second law.
  • #1
Daniel2244
125
5

Homework Statement


I've recently watched a video which explains Kirchhoff's first law however, I'm not sure about his calculations. I got the same answer just wanting to make sure I am doing it right. the guy wrote L1: -75I2 +3V=0 ⇒ I2= -3/-75=0.04A
He calculated L2 like -12V -125I3 +75I2=0 ⇒ -12 -125I3 + 75(0.04)=0 ⇒ -12 - 125I3 +3=0⇒ I3=12-3.0/-125=0.072A
Another question, does this -12V -125I3 +75I2=0 equal zero becasue of Kirchhoff's second law?

Homework Equations


I1=I2+I3

The Attempt at a Solution


starting in the top left corner - L1: -75I2 +3V=0 ⇒ 3V=75I2⇒ 3/75=75I2/75⇒ I2=3/75=0.04A

starting at J1 - L2: -12V -125I3 +75I2=0 ⇒ -12V+75I2=125I3 ⇒ I3=-12+(75x0.04)/125= -0.072A

Using equation I1=I2+I3⇒ I1=0.04+0.072= -0.032A (-=current going wrong way)

*Stupid question I know but just want to make sure
 

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  • #2
Your method and results look fine to me.
 
  • #3
gneill said:
Your method and results look fine to me.
Thanks for letting me know .
 
  • #4
gneill said:
Your method and results look fine to me.
A quick question, If L1 and L2 were going anti clockwase would the equation still be I1=I2+I3? Nvm yes it would. However, If the current was going anti clockwise do we need to the circuit look anti clock wise?
 
  • #5
Daniel2244 said:
However, If the current was going anti clockwise do we need to the circuit look anti clock wise?
Not sure what you're asking there, but the bottom line is that it doesn't make any difference which way you define your initial current directions so long as you are consistent in determining the potential drop directions due to those current. The math will always take care of itself.
 
  • #6
gneill said:
Not sure what you're asking there, but the bottom line is that it doesn't make any difference which way you define your initial current directions so long as you are consistent in determining the potential drop directions due to those current. The math will always take care of itself.
Ok, does this -12V -125I3 +75I2=0 equal zero becasue of kirchhoff's second law?
 
  • #7
Daniel2244 said:
Ok, does this -12V -125I3 +75I2=0 equal zero becasue of kirchhoff's second law?
Presumably by Kirchhoff's 2nd law you are referring to KVL, so yes, taking your defined current directions from your image that is the case.
 

1. What is Kirchhoff's First Law?

Kirchhoff's First Law, also known as the "Law of Conservation of Charge," states that the total current entering a junction in a circuit is equal to the total current leaving that junction.

2. How does Kirchhoff's First Law apply to circuits with 2 loops?

In a circuit with 2 loops, Kirchhoff's First Law still applies. The total current entering a junction in one loop must be equal to the total current leaving that junction in the same loop and in the other loop.

3. How do I use Kirchhoff's First Law to solve a circuit with 2 loops?

To solve a circuit with 2 loops, you must first identify all the junctions in the circuit. Then, use Kirchhoff's First Law to write equations for each junction, setting the sum of incoming currents equal to the sum of outgoing currents. Finally, solve the system of equations to find the unknown currents in the circuit.

4. What is the purpose of using Kirchhoff's First Law in circuit analysis?

Kirchhoff's First Law allows us to apply the principle of conservation of charge to circuits, ensuring that our calculations are accurate. It also helps us to determine the unknown currents in a circuit, which is essential for designing and troubleshooting electrical systems.

5. Are there any limitations to Kirchhoff's First Law?

Kirchhoff's First Law is based on the assumption that the circuit is in a steady state, meaning that the currents, voltages, and resistances do not change over time. It also assumes that the junctions in the circuit are ideal, with no resistance or capacitance. In reality, these ideal conditions may not always be met, and therefore, the application of Kirchhoff's First Law may not always yield accurate results.

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