How can Kirchhoff's Laws be used to solve for current in a circuit?

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In summary, the conversation discusses the use of KVL and KCL in a circuit and the difficulty in obtaining results. The suggestion is made to eliminate a shorted resistor and redraw the circuit, using nodal analysis or Kirchhoff's laws to solve for the unknown voltages and currents. Sample values for the branch currents are also provided.
  • #1
NatsuIgneelFT
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Homework Statement
Use KVL and KCL to determine all voltages and currents through each resistor, and determine current in source.
Relevant Equations
All given is the power source is 5V. All the other elements are resistors (in ohms).
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I've been trying to use KVL/KCL here but I can't get any. The only thing I accomplished is R6 has 0V, 0A (KVL with its loop). All the other ones I can't get any? Thanks
 
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  • #2
Welcome to the PF.:smile:

You are correct that R6 is shorted out, so eliminate it from the drawing. You can re-draw it a little more cleanly with the 5V source vertical with its bottom considered a common "ground". When I do that it looks like a bridge circuit, so label the 3 voltages at the 3 nodes (not including ground) and write the KCL equations. Can you show us that work?
 
  • #3
IMG_20190903_230918.jpg


Thank you. Is this how to do it? I still can't see any patterns here, sorry.
 
  • #4
Label the unknown voltages on the 3 right nodes and write the KCL equations for them. Then see if you have enough equations to solve for the unknown voltages. Once you have the node voltages, that gives you the branch currents...
 
  • #5
Kirchoff or nodal.jpg

Attach currents to all resistors -for instance I1 through R1 and so on.

For nodal analyze name X and Y the potentials as per attached sketch.

For Kirchhoff way you have 3 loops:

abdfa, abcefa, abdefa

and two current sum points: d and e

I1=0.03852;I2=0.015485;I3=0.0171638;I4=0.02135755;I5=0.032649
 

FAQ: How can Kirchhoff's Laws be used to solve for current in a circuit?

1. What are Kirchhoff's Laws?

Kirchhoff's Laws are a set of principles used to analyze and solve electrical circuits. They were developed by German physicist Gustav Kirchhoff in the mid-19th century and are still widely used in modern circuit analysis.

2. What is the first law of Kirchhoff?

The first law, also known as Kirchhoff's Current Law (KCL), states that the total current entering a junction in a circuit must equal the total current leaving that junction. In other words, the amount of current flowing into a point must equal the amount of current flowing out of that point.

3. What is the second law of Kirchhoff?

The second law, also known as Kirchhoff's Voltage Law (KVL), states that the sum of all voltages around a closed loop in a circuit must equal zero. This means that the voltage drops across all elements in a closed loop must equal the voltage gains in that loop.

4. How do you use Kirchhoff's Laws to solve a circuit?

To solve a circuit using Kirchhoff's Laws, you first need to draw a circuit diagram and label all the components and their values. Then, you can apply KCL and KVL to write a set of simultaneous equations. These equations can be solved using algebraic methods to find the values of current and voltage in the circuit.

5. Can Kirchhoff's Laws be used for any type of circuit?

Yes, Kirchhoff's Laws can be applied to any type of circuit, including DC and AC circuits. They can also be used for both series and parallel circuits. However, in some cases, their application may become more complex, and other techniques may need to be used in combination with Kirchhoff's Laws.

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