# Korkhoff's Loop Rule: Proving Current Ratios

• okgo
In summary, the helpful yahoo user explained that the total current is 1.45 amps, with 0.87 amps flowing through the 2Ω resistor and 0.58 amps through the 3Ω resistor. They also mentioned that this can be understood intuitively due to current taking the path of least resistance. They advised to avoid using numbers in solving problems that do not require them.
okgo
http://www.screencast.com/users/trinhn812/folders/Jing/media/3bedaa97-7020-4c5b-85d8-213de24b30a5

For the above problem. A helpful yahoo user told me that I can prove the answer for the above question by solving the problem. He said:

Total current is 9/6.2 = 1.45 amps.
that all flows thru the 5Ω, and 3/5 of that goes thru the 2Ω (0.87) and 2/5 thru the 3Ω (0.58).

So I understand how to prove that his ratio is correct with Korkhoff's loop rule.

But I was wondering how he got the ratio 3/5 for the current of the 2Ω and 2/5 for the 3Ω resistors without using the loop rule. Is it just intuitive?

Last edited:
Yes, it is just intuitive, but it may take awhile to develop circuit intuition before you can get there yourself. Current takes the path of least resistance (or impedance if you get really far into circuits). Don't even use numbers to solve a problem that doesn't need them. :)

## 1. What is Korkhoff's Loop Rule?

Korkhoff's Loop Rule, also known as Kirchhoff's Voltage Law, states that the sum of the voltage drops in a closed electrical circuit is equal to the total voltage supplied by the source.

## 2. How does Korkhoff's Loop Rule relate to current ratios?

Korkhoff's Loop Rule can be used to prove the current ratios in a circuit by applying it to each individual loop in the circuit. By setting the sum of the voltage drops in each loop equal to the total voltage supplied, the current ratios can be derived.

## 3. What is the significance of proving current ratios?

Proving current ratios is important in understanding the flow of current in a circuit and can help in designing and troubleshooting electrical systems. It also allows for the calculation of voltage drops and power dissipation in different components of the circuit.

## 4. Are there any limitations to using Korkhoff's Loop Rule?

Korkhoff's Loop Rule assumes that the circuit is in a steady state and that there are no changing magnetic fields. It also does not take into account the resistance of the wires in the circuit, which can affect the accuracy of the results.

## 5. How do you apply Korkhoff's Loop Rule to a circuit?

To apply Korkhoff's Loop Rule, you must first identify all the loops in the circuit. Then, for each loop, assign a direction of current flow and label the voltage drops and the voltage sources. Finally, write an equation using the rule for each loop and solve for the current ratios.

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