Solve KCL/MESH Problem: E=15V, R1=20k, R2=4.7k, R3=10k

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In summary, the problem involves finding the currents I1, I2, and I3 in a circuit with a 15V power supply and resistors R1=20k ohms, R2=4.7k ohms, and R3=10k ohms. The equations used to solve this problem are KVL (Kirchhoff's Voltage Law) and Norton's Theorem. KCL (Kirchhoff's Current Law) can also be used to simplify the equations.
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thorwynn
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Homework Statement



circuit-1.jpg


Determine I_1 I_2 I_3
When
E = 15V
R1 = 20k ohms
R2 = 4.7k ohms
R3 = 10k ohms

Homework Equations



KCL equation

The Attempt at a Solution



i tried to find using KCL.. is my equation right?
Loop equation 1:
EB + I3R3 + R1(I3 + I1) = 0

Loop equation 2:
R1(I1 + I3) + R2(I1 – I2) = 0

Loop equation 3:
EB + I3R3 + I2R2 = 0

can i use MESH analysis... but there are three unknowns and if i use mesh, i can only have 2 equations with 3 unknowns
 
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  • #2
Welcome to PF.

There is a problem with your equations.

The voltage across R1 is is simply R1*I1, not R1(I1 + I3), because the current flowing through R1 is simply I1.

Likewise, the voltage across R2 is R2*I2.

Also, these are KVL equations for voltage, not KCL which would apply to currents. KCL says that the sum of all currents entering a node is zero, and will be useful here.

Note, another way to solve this would be to use the rules for combining resistors in parallel and series.
 
  • #3
I agree with Redbelly98, I think you're confusing KVL for KCL. See if you can combine the resistors to find the current coming out of the supply. From there, I think it's easier if you find the http://en.wikipedia.org/wiki/Norton_equivalent" equations. See link for quick wikipedia articles on them. Mesh analysis will work just fine here as well, but I think it's more obvious using Norton equivalent.
 
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  • #4
u can apply kvl at the 2mishes and get 2equa., in 2variables .then solve them
 

1. What is KCL and MESH in circuit analysis?

KCL (Kirchhoff's Current Law) and MESH (Mesh Analysis) are two methods used in circuit analysis to solve for unknown currents and voltages in a circuit. KCL states that the sum of currents entering and exiting a node in a circuit must be equal, while MESH uses loop equations to solve for current and voltage values in a circuit.

2. How do I apply KCL and MESH in a circuit problem?

To solve a circuit problem using KCL and MESH, you first need to identify the nodes and loops in the circuit. Then, apply KCL at each node to write equations for all the unknown currents. Next, use MESH to write loop equations and solve for the unknown currents and voltages using simultaneous equations.

3. What is E in the given circuit problem?

In this circuit problem, E represents the voltage source with a value of 15V. This means that the voltage at that point in the circuit is 15V, and it remains constant.

4. How do I calculate the equivalent resistance in this circuit?

To calculate the equivalent resistance in this circuit, you can use the formula 1/R = 1/R1 + 1/R2 + 1/R3, where R1, R2, and R3 are the resistances in the circuit. In this case, the equivalent resistance would be 3.7k.

5. Can KCL and MESH be used in all circuit problems?

Yes, KCL and MESH can be used in almost all circuit problems, as long as the circuit is linear and has a finite number of nodes and loops. These methods are commonly used in circuit analysis because they provide an efficient and systematic way to solve for unknown currents and voltages.

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