Determine current using Kirchoff's Junction/Loop Rule

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In summary, using Kirchhoff's Loop and Junction Rules, we can determine the currents i1, i2, and i3 flowing through R1, R2, and R3, respectively, in the given circuit. By summing the equations and using Ohm's Law, we can find the value of i3. The last equation in the attempt at a solution is not necessary.
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Renaldo
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Homework Statement



In the circuit shown in the figure, R1 = 6 Ω, R2 = 13 Ω, and R3 = 19 Ω, Vemf,1 = 10 V, and Vemf,2 = 15 V. Using Kirchhoff's Loop and Junction Rules, determine the currents i1, i2, and i3 flowing through R1, R2 and R3, respectively, in the direction indicated in the figure.



Homework Equations



i1 + 12 = 13

V=IR


The Attempt at a Solution



i1 + 12 = i3

V1 + I3R3 + I1R1 = 0

V2 + I2R2 + I3R3 = 0

I1 = (-V1 - I3R3)/R1

I2 = (-V2 - I3R3)/R2

I3 = (-V1 - I1R1)/R3

Does this look right?
 

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  • #2
The last equation leads you nowhere. Instead, sum the two previous equations, that, together with the first equation, will give you an equation from which you will be able to find I3.
 
  • #3
Thanks. I was able to solve it.
 

1. What is Kirchoff's Junction/Loop Rule?

Kirchoff's Junction/Loop Rule is a fundamental principle in circuit analysis that states that the sum of the currents entering a junction in a circuit must equal the sum of the currents leaving the junction. It also 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 do I use Kirchoff's Junction/Loop Rule to determine current?

To use Kirchoff's Junction/Loop Rule, you must first draw a circuit diagram and label all the junctions and loops. Then, at each junction, write an equation that sets the sum of the entering currents equal to the sum of the leaving currents. Next, for each closed loop, write an equation that sets the sum of the voltage drops equal to the sum of the voltage sources. Finally, solve the resulting system of equations to determine the current in each branch of the circuit.

3. Can Kirchoff's Junction/Loop Rule be applied to any circuit?

Yes, Kirchoff's Junction/Loop Rule can be applied to any circuit, regardless of its complexity. This rule is based on the fundamental principles of conservation of charge and energy, and it is applicable to both DC and AC circuits.

4. What are the limitations of Kirchoff's Junction/Loop Rule?

Kirchoff's Junction/Loop Rule assumes that the circuit is in a steady state and that the components are ideal, meaning they have no resistance or capacitance. It also assumes that the circuit is linear, meaning the voltage and current relationships are proportional. These assumptions may not hold true in all real-world circuits, which can limit the accuracy of the results obtained using this rule.

5. How is Kirchoff's Junction/Loop Rule related to Ohm's Law?

Kirchoff's Junction/Loop Rule is not directly related to Ohm's Law. However, both are fundamental principles in circuit analysis and can be used together to solve for unknown variables in a circuit. Ohm's Law states that the voltage across a resistor is equal to the current through the resistor multiplied by its resistance, while Kirchoff's Junction/Loop Rule helps to determine the current in each branch of a circuit.

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