How Do You Calculate I_2 and I_4 Using Kirchoff's Rules?

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In summary, using Kirchoff's Rules, the values of the currents I_2 and I_4 were found to be 2.2 A and 1.20 A, respectively, in a circuit with a given current of 1.6 A and resistors of varying values. The solution involved using the loop rule in the smaller loop and then in the larger loop to solve for the unknown currents.
  • #1
ttiger2k7
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[SOLVED] Using Kirchoff's Rules

Homework Statement



http://img266.imageshack.us/img266/4120/kirchoffho1.gif
In the circuit, I_1 = 1.6 A. Find the value of: (a) the current I_2 and (b) the current I_4.

Homework Equations



Junction Rule, Loop Rule, V=IR

The Attempt at a Solution



Small loop, top left:

2V + (2ohms)(I_2) - (4ohms)(1.6 A) = 0
(2 ohms)(I_2) - (6.4) = -2
2 ohms * I_2 = 4.4
I_2 = 2.2 A

That also means that the current in the entire circuit is 4.4 Amps.

...Right?

That is as far as I got. Assuming my answer for I_2 is correct, all I have to do is find I_4, which I am stumped on how to do. Should I combine the two resistors on the top left, since they're in series?

Homework Statement


Homework Equations


The Attempt at a Solution

 
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  • #2
Small loop, top left:(moving anti-clockwise)

[tex] 2+ 4*1.6-2i_2=0[/tex]
[tex]i_2 =4.2 A[/tex]

Should I combine the two resistors on the top left, since they're in series?

I don't think any two resistors in this circuit are in series :redface:
 
  • #3
So that means, I got something that *roughly* looks like the following:

http://img297.imageshack.us/img297/7287/kirchoffeditck6.gif
(horrible MS paint editting by me)

So that means total I will be 5.8 (1.6 + 4.2).

Should I now do a loop rule for the whole circuit, calling the smaller loop Ir (where r is the total resistence of the right loop)? Then just solve for R using r and I?
 
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  • #4
So that means, I got something that *roughly* looks like the following

No I don't think so. The resistances are neither in series nor parallel. You'll have to use KVL.
Should I now do a loop rule for the whole circuit, calling the smaller loop Ir (where r is the total resistence of the right loop)? Then just solve for R using r and I?

In the circuit, I_1 = 1.6 A. Find the value of: (a) the current I_2 and (b) the current I_4.

The question doesn't ask you to find R. Only [tex]i_2[/tex] and [tex]i_4[/tex]
Just use loop rule in lower big loop to find [tex]i_4[/tex] .
 
  • #5
Thanks. Got it!

12 V - 4.2*2 - 3I_4 = 0

I_4 = 1.20 A
 

FAQ: How Do You Calculate I_2 and I_4 Using Kirchoff's Rules?

What are Kirchoff's Rules?

Kirchoff's Rules are a set of fundamental principles in circuit analysis that are used to determine the voltage and current in different parts of an electrical circuit. They are named after Gustav Kirchoff, a German physicist who first introduced them in the mid-19th century.

Why are Kirchoff's Rules important?

Kirchoff's Rules are important because they provide a systematic approach to analyzing complex electrical circuits. By following these rules, scientists and engineers can accurately determine the behavior of a circuit and predict the flow of current and voltage at different points.

What are the two rules in Kirchoff's Rules?

The two rules in Kirchoff's Rules are the Kirchoff's Current Law (KCL) and Kirchoff's Voltage Law (KVL). KCL states that the sum of all currents entering and exiting a node in a circuit must be equal to zero. KVL states that the sum of all voltage drops in a closed loop must be equal to the sum of all voltage sources in that loop.

How do you use Kirchoff's Rules to solve a circuit?

To solve a circuit using Kirchoff's Rules, first identify all the nodes and loops in the circuit. Then, apply KCL at each node and write an equation for the sum of all currents entering and exiting that node. Next, apply KVL to each loop and write an equation for the sum of all voltage drops and sources in that loop. Finally, solve the system of equations to find the unknown currents and voltages in the circuit.

Are there any limitations to using Kirchoff's Rules?

Yes, there are some limitations to using Kirchoff's Rules. These rules assume that the circuit is in a steady-state, meaning that all currents and voltages are constant. They also assume that the circuit is linear, meaning that the components do not have any non-linear characteristics. Additionally, Kirchoff's Rules may become more complex to apply in circuits with a large number of nodes and loops.

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