Kirchhoff's law: Find the current I3 through the Amp meter

  • #1
skibidi
10
0
Homework Statement
Find the current I3,I2, and I1 through the Amp meter.
Answer in units of A.
Relevant Equations
I used the Junction Rule - I3= I1+I2
I separated the circuit into parts- upper and lower

For the upper loop I wrote: -14-2I1-3.4I3-I2 = 0
For the lower loop I wrote 16-2.9I2+3.4I3-5.4I2 = 0

I solved for I1 and I2 separately and plugged it into the junction rule and solved for I3.

I may have got it wrong because of the incorporation of the extra resistor in the upper loop and lower loop and solved incorrectly.

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  • #2
Correction for the problem after i found I3 correctly now.

The correct equation is now -14+3.3(I1)+3.4(I3)+2(I1)= 0 for the upper loop and
-16+5.3(I2)-3.4(I3)+2.9(I2) = 0 for the bottom loop. Once you separate variables, I2 = stuff and I1 = stuff, you can use the junction rule I1 = I2+I3 and rearrange to get I1-I2=I3. Plug it in and you should get I3 = 0.336A
 
  • #3
Use I3 to get I2 and I1 since you have separate equations for them already -

I1 = -3.4(I3)+14/5.3 and I2 = 3.4(I3) +16/ 8.2

I1 = 2.43 A , I2 = 2.09 A
 
  • #4
If anyone else sees this, can you verify that my explanation is correct since I was able to get the correct answers on my own.
 
  • #5
## \text { The explanation is correct, but the result can be more accurate. } ##

## 3,3 \Omega \cdot 2,43 A + ( - 14 ) V + 2 \Omega \cdot 2,43 A + 3,4 \Omega \cdot 0,336 A = ##
## = 8,0058 V – 14 V + 4,852 V + 1,1424 V = ##
## = 0,0214 V \neq 0 V ##
## \text { It is hard to say that Kirchhoff Voltage Law is satisfied for the upper loop because it is hard to say that } 0,0214 V \text { is equal to } 0 V \text { . } ##
## \text { The more accurate result can be got rounding the value of } I _ 1 \text { to } 2,426 A \text { instead of } 2,43 A \text { . } ##
## \text { Values of } I _ 2 \text { , which is } 2,090 A \text { , and } I _ 3 \text { , which is } 0,336 A \text { , can remain the same. } ##
 

FAQ: Kirchhoff's law: Find the current I3 through the Amp meter

1. What is Kirchhoff's Current Law (KCL) and how does it apply to finding I3?

Kirchhoff's Current Law (KCL) states that the total current entering a junction must equal the total current leaving the junction. To find I3, you can set up an equation based on the currents entering and leaving the nodes in the circuit. This will help you solve for the unknown current I3 through the Amp meter.

2. What is Kirchhoff's Voltage Law (KVL) and how can it be used to determine I3?

Kirchhoff's Voltage Law (KVL) states that the sum of all voltages around a closed loop must equal zero. By applying KVL to loops in the circuit, you can create equations that relate the various currents and resistances. Solving these equations simultaneously with KCL can help you find the current I3.

3. How do I set up the equations to solve for I3 using Kirchhoff's laws?

First, identify all the nodes and loops in the circuit. Apply KCL at each node to get equations for the currents. Next, apply KVL to each independent loop to get equations for the voltages. Combine these equations to create a system of linear equations that can be solved for the unknown currents, including I3.

4. What are the common mistakes to avoid when using Kirchhoff's laws to find I3?

Common mistakes include not correctly identifying all the nodes and loops, neglecting the sign conventions for voltage drops and rises, and not accounting for all currents at a junction. Ensure that you carefully follow the sign conventions and double-check your equations for consistency.

5. Can Kirchhoff's laws be applied to both AC and DC circuits to find I3?

Yes, Kirchhoff's laws can be applied to both AC and DC circuits. However, for AC circuits, you must also consider the phase angles of the voltages and currents, and use complex numbers to represent them. The fundamental principles remain the same, but the calculations involve additional complexity due to the alternating nature of the currents and voltages.

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