# Using Kirchhoff's rules to calculate current

• trevorwisc
In summary, the conversation discusses using Kirchhoff's laws to calculate the three currents indicated in a circuit diagram. The solution attempt involves finding the values of I1, I2, and I3 through a series of equations. However, it is also important to apply Kirchhoff's current law at the nodes where currents join and split. The summary ends with a reminder to label the net currents on wires around the nodes in order to accurately calculate the desired currents.
trevorwisc
1. Calculate the three currents indicated in the circuit diagram below.

I have attached the diagram.

How would I use Kirchhoff's laws to find the currents I am getting thrown off by the third loop.

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trevorwisc said:
1. Calculate the three currents indicated in the circuit diagram below.

I have attached the diagram.

How would I use Kirchhoff's laws to find the currents I am getting thrown off by the third loop.

How are you "getting thrown off by the third loop"? You'll have to show your attempt at a solution so we can see how to help.

gneill said:
How are you "getting thrown off by the third loop"? You'll have to show your attempt at a solution so we can see how to help.

Solution attempt:

I1 loop 9.00V-9.00(I1)=0 so I1=1A
I2 loop 12.00v-6.00(I2)=0 so I2=2A
For I3 loop 12.00V-10(I3)-8(I1)-1(I2)=0 by plugging in I1 and I2 I get I3 to be 5A.

trevorwisc said:
Solution attempt:

I1 loop 9.00V-9.00(I1)=0 so I1=1A
I2 loop 12.00v-6.00(I2)=0 so I2=2A
For I3 loop 12.00V-10(I3)-8(I1)-1(I2)=0 by plugging in I1 and I2 I get I3 to be 5A.

Ah. Don't forget to apply KCL at the nodes where currents join/split. For the "I1 loop", for example, I3 joins the party at the rightmost node, so the current through the 8.00 Ohm resistor is actually I1 + I3. Label the net currents on wires around the nodes.

To calculate the three currents in the circuit diagram using Kirchhoff's rules, we would first apply Kirchhoff's Current Law (KCL) at each junction in the circuit. This law states that the sum of all currents entering a junction must be equal to the sum of all currents leaving the junction.

Starting at the top junction, we can label the current entering as I1 and the currents leaving as I2 and I3. Applying KCL, we get the equation I1 = I2 + I3.

Next, we can apply Kirchhoff's Voltage Law (KVL) in each closed loop of the circuit. This law states that the sum of all voltage drops in a closed loop must be equal to the sum of all voltage sources in the loop.

For the first loop, we can label the voltage drops as V1 and V2 and the voltage source as V. Applying KVL, we get the equation V1 + V2 = V.

For the second loop, we can label the voltage drops as V3 and V4 and the voltage source as V. Applying KVL, we get the equation V3 + V4 = V.

Now, we have three equations (I1 = I2 + I3, V1 + V2 = V, V3 + V4 = V) with three unknowns (I1, I2, I3). By solving these equations simultaneously, we can find the values of the three currents.

As for the third loop that is throwing you off, you can simply ignore it when applying KVL as it does not have any voltage sources or drops. However, you will need to consider it when applying KCL at the bottom junction. You can label the current in the third loop as I4 and apply KCL at the bottom junction to get the equation I3 = I4.

I hope this helps you in calculating the currents using Kirchhoff's rules.

## 1. What are Kirchhoff's rules?

Kirchhoff's rules, also known as Kirchhoff's laws, are a set of fundamental principles used to analyze electric circuits. These rules are based on the law of conservation of charge and energy and are essential for calculating current in a circuit.

## 2. What is the first rule of Kirchhoff's rules?

The first rule, also known as Kirchhoff's current law (KCL), states that the sum of the currents entering a junction in a circuit must equal the sum of the currents leaving the junction. This law is based on the principle of conservation of charge.

## 3. What is the second rule of Kirchhoff's rules?

The second rule, also known as Kirchhoff's voltage law (KVL), states that the sum of the voltage drops (or rises) around a closed loop in a circuit must equal the sum of the voltage sources in that loop. This law is based on the principle of conservation of energy.

## 4. How do I apply Kirchhoff's rules to calculate current?

To calculate current using Kirchhoff's rules, you first need to draw a circuit diagram and label all the components and their values. Then, use KCL to set up equations for the currents at each junction and use KVL to set up equations for the voltage drops in each loop. Finally, solve the equations simultaneously to find the current in each branch of the circuit.

## 5. Are there any limitations to using Kirchhoff's rules?

While Kirchhoff's rules are powerful tools for analyzing electric circuits, they do have some limitations. They assume that the circuit is in a steady-state and that all components are ideal. In reality, circuits may have time-varying elements or non-ideal components, which can lead to some inaccuracies in the calculations. Additionally, Kirchhoff's rules are based on linear circuit analysis, so they may not be applicable to non-linear circuits.

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