- #1
shibuzgeorge
- 6
- 1
Homework Statement
Homework Equations
Using Loop 1, 2 and 3
berkeman said:Welcome to the PF.
Things look okay so far to me. You still need to plug the equation for I2 into your equation for I1, and then the equation for I3 also gets combined. The result they want you to show only has the values of the voltage sources and resistances in it.
vela said:Only two of the loop equations are useful. The third one isn't independent; if you add the equations for loop 1 and loop 2 together, you get the equation for loop 3. So solve the system consisting of two of the loop equations and the KCL equation.
At this point, it's algebra. You've likely solved this kind of problem before: 3 equations, 3 unknowns. It just doesn't look familiar because you're not using the variables x, y, and z.
vela said:Can you solve a problem like the following? (Not asking you to solve it, but do you know what to do?)
\begin{align*}
2x + y &= 6 \\
-x + 2y &= 0
\end{align*}
How about this?
$$\begin{align*}
2x + 3y &= 2 \\
4y-2z &= 0 \\
-3x + 5z &= 10
\end{align*}$$
kuruman said:Here is another strategy. You have three equations. One of them is KCL ##I_1=I_2+I_3##. OK, replace all occurrences of ##I_1## with ##(I_2 + I_3)## in the two KVL equations. You will get two equations having unknowns ##I_2##, ##I_3##. Solve one of them to find ##I_2## in terms of ##I_3##. Replace the expression for ##I_2## that you get in the other equation. This will give you a single equation with ##I_3## as the only unknown. Solve it. Then go back and find ##I_2## and finally go back and find ##I_1##. There are less cumbersome ways of getting to the answer as other have suggested, but this is straightforward and easy to understand.
Kirchoff's Voltage Law (KVL) states that the sum of all voltages in a closed loop circuit must equal zero. This means that the voltage drops across all components in a circuit must add up to the voltage supplied by the source.
Kirchoff's Current Law (KCL) states that the total current flowing into a junction in a circuit must equal the total current flowing out of that junction. In other words, the amount of current entering a junction must be equal to the amount of current leaving that junction.
Kirchoff's Laws are fundamental principles in circuit analysis, which is the process of determining how electrical components and sources behave in a given circuit. They allow us to understand and predict the behavior of complex circuits by simplifying them into simpler parts and using these laws to find the relationship between the different components.
Yes, Kirchoff's Laws can be applied to both DC (direct current) and AC (alternating current) circuits. These laws are based on the principles of conservation of energy and conservation of charge, which hold true for both types of circuits.
Kirchoff's Laws have many practical applications in industries such as electronics, electrical engineering, and telecommunications. They are used to design and analyze circuits in various devices such as computers, televisions, and smartphones. They are also used in power systems to ensure that electricity is distributed efficiently and safely.