Circuit Analysis: Find i, v Given R1, R2

In summary, the problem involves finding the current and voltage in a circuit with resistors R_1 = 6 ohms and R_2 = 3 ohms. Using Kirchhoff's laws and Ohm's law, the current i was found to be 1A and the voltage v was found to be 12V. However, further analysis showed that these values may not be correct as the voltage source may be absorbing power instead of supplying it. The correct approach may involve using KVL for the left and right loops and considering the current through R_1 as the sum of the left and right loop currents.
  • #1
Xkaliber
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0

Homework Statement



(a) Suppose that R_1 = 6 ohms and R_2 = 3 ohms. Find the current i and the voltage v. See the diagram in the picture.

http://img291.imageshack.us/img291/7638/picturewr3.th.jpg

Homework Equations



Kirchhoff's laws and Ohm's law

The Attempt at a Solution



I got v=12V and i=1A

However, I do not think that this is correct since a positive value for i means the voltage source is absorbing energy instead of supplying it, which does not make sense.
 
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  • #2
Xkaliber said:
I got v=12V and i=1A

However, I do not think that this is correct since a positive value for i means the voltage source is absorbing energy instead of supplying it, which does not make sense.

Why don't you write out your current loop equations and maybe we can see where you may be confused?
 
  • #3
First, since the 3 amp current source is in series with R_2, the current through R_2 is 3A. Using Ohm's law, we find the voltage across R_2 to be 9 volts.

Now, KVL around outer loop: -12V - 9V + v = 0 -> v = 21V

KVL around right smaller loop: -9V + 21V - v_1 = 0 -> v_1 = 12V

Using ohm's law, current through R_1 = 2A

KCL @ top middle node: 3A - 2A - i = 0 -> i = 1A

If i does equal 1A, then according to the diagram in the picture, the voltage source is absorbing power since it is in the passive convention.
 
  • #4
Xkaliber said:
Now, KVL around outer loop:

This could be your problem.

I think what you really want to do is take the equations for the left and right loops, noting that the current through the R1 is the sum of the left and right loop currents.

This should give ou the equations and unknowns that you are looking for.
 

FAQ: Circuit Analysis: Find i, v Given R1, R2

1. What is circuit analysis?

Circuit analysis is the process of analyzing electrical circuits to determine the behavior of current, voltage, and power in the circuit. This involves using mathematical equations and laws, such as Ohm's Law and Kirchhoff's Laws, to calculate and predict the values of current and voltage at different points in the circuit.

2. How do you find current and voltage in a circuit?

To find the current and voltage in a circuit, you need to use Ohm's Law (V=IR) and Kirchhoff's Laws. Ohm's Law allows you to calculate the voltage (V) across a component by multiplying its resistance (R) by the current (I) flowing through it. Kirchhoff's Laws help you analyze complex circuits by applying the principle of conservation of energy and charge.

3. What is the purpose of using resistance values (R1, R2) in circuit analysis?

Resistance values (R1, R2) are used in circuit analysis to represent the amount of opposition to current flow in a circuit. The higher the resistance, the lower the current will be. By knowing the values of resistance, you can calculate the voltage and current in different parts of the circuit using Ohm's Law.

4. How do you approach circuit analysis problems?

To approach circuit analysis problems, you should first draw a schematic diagram of the circuit and label all the components and their values. Then, apply Kirchhoff's Laws and Ohm's Law to write equations and solve for the unknown values. It is important to simplify the circuit as much as possible by using series and parallel equivalent circuits to make the calculations easier.

5. Can circuit analysis be applied to real-world circuits?

Yes, circuit analysis can be applied to real-world circuits. In fact, it is a crucial tool for designing and troubleshooting electronic circuits in various industries, such as telecommunications, power systems, and consumer electronics. By using circuit analysis, engineers can predict and optimize the performance of real-world circuits before they are built.

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