# Kirchhoff's Laws and current through resistors

• Vashti
In summary: Similarly with the loop equations, if all voltage arrows are in the right direction, then the voltage value is positive, otherwise it is negative.In summary, the conversation discusses the process of solving a circuit with three unknowns using three equations. The equations involve loop equations for the voltages and a current equation. The current direction must be taken into account when setting up the equations, with negative values indicating opposite current direction.

#### Vashti

Question:

The diagram below shows a circuit where; R1 = 5.00 Ω, R2 = 6.00 Ω, R3 = 1.00 Ω, V1 = 4.500 V, V2 = 20.00 V, and V3 = 6.00 V. (In solving the problems that follow, initially pick the current directions as shown. If the actual current turns out to be in the opposite direction, then your answer will be negative).
What is the value of I1? I2? I3?

Attempts:

So I know that I need three equations to solve it as I have three unknowns. I tried to make one using the junction where I2 meets I1 and I3, but they all come together and kind of crash, so I don't know how to put that into equation form any more :( I'm assuming I need to do loops to get the other two equations but again I run into the issue of knowing how to set them up. If I try to make points on either side of each resistor they won't 'flow' really...
In summary I am just very confused, so any help is welcome!

Thanks!

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There are two loop equations for the voltages around each loop, and there is one current equation.

Sum if currents (net) into a node is zero, so I1+I2+I3=0, because what goes in must come out, otherwise there is a net charge accumulation. If all current arrows go into a node, then one must be negative, i.e. the current is opposite the arrow.

Hi there,

It seems like you are on the right track with using Kirchhoff's Laws to solve this circuit. To set up the equations, you can use Kirchhoff's Current Law (KCL) at the junction where I2 meets I1 and I3. This law states that the sum of the currents entering a junction must equal the sum of the currents leaving the junction. So for this junction, the equation would be:

I2 + I3 = I1

To get the other two equations, you can use Kirchhoff's Voltage Law (KVL) around each loop in the circuit. This law states that the sum of the voltage drops around a closed loop must equal the sum of the voltage rises. So for the first loop, using the current direction shown, the equation would be:

V1 - R1*I1 - V2 = 0

And for the second loop, the equation would be:

V2 - V3 - R2*I2 - R3*I3 = 0

From here, you can solve the system of equations to find the values of I1, I2, and I3. Remember that if the actual current turns out to be in the opposite direction, your answer will be negative, so be sure to check your final values.

I hope this helps! Let me know if you have any other questions or if you need further clarification. Good luck!

## 1. What are Kirchhoff's Laws?

Kirchhoff's Laws are two fundamental laws in circuit analysis that govern the behavior of electrical current and voltage in a closed circuit. The first law, also known as Kirchhoff's Current Law, states that the total current entering a junction must equal the total current leaving the junction. The second law, known as Kirchhoff's Voltage Law, states that the sum of the voltage drops in a closed loop must equal the sum of the voltage sources in that loop.

## 2. How are Kirchhoff's Laws used in circuit analysis?

Kirchhoff's Laws are used to solve for the unknown currents and voltages in a closed circuit. By applying the laws to a circuit diagram and setting up equations based on the known values and components, the unknown values can be solved using algebraic methods.

## 3. What is the relationship between current and resistance in a circuit?

According to Ohm's Law, the relationship between current and resistance is inverse. This means that as resistance increases, current decreases, and vice versa. This relationship is based on the equation: I = V/R, where I is current, V is voltage, and R is resistance.

## 4. How is current divided in a circuit with multiple resistors?

In a series circuit, the current through each resistor is the same, as the current has only one path to flow through. In a parallel circuit, the current is divided among the branches based on the resistance of each branch. The branch with the least resistance will have the most current flowing through it.

## 5. What factors affect the current through a resistor?

The current through a resistor is affected by the voltage applied and the resistance of the resistor. The higher the voltage applied, the higher the current will be. Similarly, the higher the resistance, the lower the current will be. Temperature also affects the current through a resistor, as an increase in temperature can increase the resistance and decrease the current.

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