Why Are My Kirchhoff Voltage Rule Equations Incorrect?

In summary, the conversation is about a person trying to solve a circuit with three loops and encountering issues with summing the currents correctly. They have attached an image of the problem and are questioning the validity of including certain terms in their calculations. They are advised to make sure that charge is also conserved in order to solve the circuit successfully.
  • #1
bob1352
6
1
Homework Statement
Just for practice, not for any assignment
Relevant Equations
Kirchhoff Voltage Rule, Sum of Voltage Drops in Loop is Equal to Zero.
I tried doing three loops. For the bottom I did 9-I1(1) + I2(1) - I3(10) -12 = 0, for the upper left corner I did 12 - I2(1)- I2(5) = 0, for the upper right corner I did 9 - I1(1) - I1(8) = 0. I came to I1 =1, I2 =2 and I3 = .2. This was incorrect, I don't think I am summing the currents correctly. I have attached an image of the problem.
 

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  • #2
Why do you have a term I1(8)? I1 is the current through the 1.00 Ω resistor. Is all that current also going through the 8.00 Ω resistor or does some of it split at the junction on the right? Same problem with the I2(5) term. To solve such circuits you need to make sure that charge is also conserved. This means that the net current through any junction must be zero.
 

Related to Why Are My Kirchhoff Voltage Rule Equations Incorrect?

What is Kirchhoff's Voltage Rule?

Kirchhoff's Voltage Rule (KVR), also known as Kirchhoff's Voltage Law (KVL), states that the sum of all electrical potential differences (voltages) around any closed loop or circuit is equal to zero. This principle is based on the conservation of energy, implying that the total energy gained per charge must equal the total energy lost per charge in a closed loop.

How do you apply Kirchhoff's Voltage Rule to a circuit?

To apply Kirchhoff's Voltage Rule, follow these steps: 1. Identify a closed loop in the circuit.2. Choose a direction to traverse the loop (clockwise or counterclockwise).3. Add the voltages across each component, taking into account their polarity (positive for a voltage rise and negative for a voltage drop).4. Set the sum of these voltages equal to zero and solve for the unknowns.

What are common mistakes when using Kirchhoff's Voltage Rule?

Common mistakes include:1. Incorrectly assigning the polarity of voltage drops and rises.2. Not including all components in the loop.3. Using inconsistent units.4. Misidentifying the direction of current flow.5. Overlooking the impact of internal resistances in power sources.

Can Kirchhoff's Voltage Rule be applied to AC circuits?

Yes, Kirchhoff's Voltage Rule can be applied to AC circuits. However, in AC circuits, voltages are typically represented as phasors, which include both magnitude and phase angle. The sum of these phasor voltages around a closed loop must still equal zero, but calculations will involve complex numbers to account for the phase relationships.

How does Kirchhoff's Voltage Rule relate to Ohm's Law?

Kirchhoff's Voltage Rule and Ohm's Law are both fundamental principles in circuit analysis. Ohm's Law states that the voltage across a resistor is equal to the product of the current through the resistor and its resistance (V = IR). When applying KVR, Ohm's Law is often used to express the voltages in terms of current and resistance, allowing for the analysis and solution of complex circuits involving multiple components.

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