Finding the current in each resistor - Kirchhoff

In summary, the conversation discusses using Kirchoff's Current Law to find the current in each resistor of a circuit with 6 loops and 4 junctions. The direction of the current can be arbitrarily labeled as long as it is consistent, and if the calculated value is negative, it simply means the current goes in the opposite direction.
  • #1
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Homework Statement



Find the current in each resistor of this circuit.

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Homework Equations



Kirchoff's Current Law

The Attempt at a Solution



I just need a nudge in the right direction. I am fairly sure Kirchoff's Current Law comes into play, and have counted 6 loops and 4 junctions. I am not sure where to proceed next; the problems we've done before with KCL usually gave us currents and their directions. Any help on getting started would be appreciated.

Thank you.
 
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  • #2
That should be the right approach -- a lot of equations, but it will all work out in the end. The strategy for the direction of the current is just to label each different current in the diagram with an arbitrary direction, as long as that direction is consistent every time you use it. So, for example, you would just say that the current across R6 points up (or down, if you want). It really doesn't matter. You'll find out in the end when you solve for the value of the current -- if the value is negative, that just means the current goes in the opposite direction of the arrow, and you happened to guess wrong, but it still conveys the same meaning.
 
  • #3
Thank you so much! That's the part I was missing: using arbitrary directions. I get it now.
 

FAQ: Finding the current in each resistor - Kirchhoff

What is Kirchhoff's Current Law?

Kirchhoff's Current Law states that the sum of all currents entering and leaving a junction in a circuit must be equal to zero. This law is based on the principle of conservation of charge.

What is Kirchhoff's Voltage Law?

Kirchhoff's Voltage Law states that the sum of all voltages in a closed loop in a circuit must be equal to zero. This law is based on the principle of conservation of energy.

How do I apply Kirchhoff's Laws to find the current in each resistor?

To apply Kirchhoff's Laws, you need to first identify all the junctions and closed loops in the circuit. Then, write down the equations for Kirchhoff's Current Law and Kirchhoff's Voltage Law for each junction and loop. Finally, solve the system of equations to find the current in each resistor.

What are the limitations of using Kirchhoff's Laws?

Kirchhoff's Laws are based on idealized assumptions and may not accurately predict the behavior of real-world circuits. They also do not account for the effects of changing magnetic fields and non-linear components, such as diodes and transistors.

Can Kirchhoff's Laws be applied to any type of circuit?

Kirchhoff's Laws are applicable to any type of circuit, including series, parallel, and complex circuits. However, they may become more complex to apply in circuits with a large number of components or non-linear elements.

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