Power Absorbed In A Electrical Circuit

[gcrawfo2]

Homework Statement

Find the power absorbed by element X, if it is 4000 Ohms.
(See attached picture for circuit)

Homework Equations

KCL: Sum of Currents into Node Must = 0

The Attempt at a Solution

I've already worked through a bunch of these type of problems, but I always mess up on which currents are positive and which ones are negative...which ultimately leads to the wrong answer. I know on this specific problem, the whole idea is to apply KCL in order to obtain a Voltage. That voltage will then be multiplied by 40 Ohms to give you the power absorbed by the resistive element.

I think my lack of understanding of KCL is keeping from getting these ideas. I guess as I run this problem through my head I use a reference location at the node above the 1000 Ohm resistor. And from my thinking I would come up with the following equation...

0=(.08)A - (v/1000[ohms])A - (.03)A - (v/4000[ohms])A

Then I would solve for V, but it ends up giving me the wrong answer. I'm assuming one of my values should be negative?

 

[gcrawfo2]

Nevermind! Figured it out. The equation above is correct, it's when I was adding and subtracting to the opposing sides, I kept seeing .08A as -.08A.

It computes out to 40V on the Resistor. Then I use P=V2/R to obtain .4 Watts.

 

[Mene]

I would suggest reviewing the concept of Kirchhoff's Current Law (KCL) and how it applies to electrical circuits. KCL states that the sum of currents entering a node (or point) in a circuit must equal the sum of currents leaving the node. In other words, the total current flowing into a node must be equal to the total current flowing out of the node.

In this problem, we can use KCL to find the voltage across element X. Let's label the node above the 1000 Ohm resistor as Node A, and the node below the 4000 Ohm resistor as Node B. Applying KCL at Node A, we get:

0 = (0.08 A) + (V_A/1000 Ohms) - (0.03 A)

Since there is no current flowing into Node A (since it is connected to the negative terminal of the voltage source), we can simplify this equation to:

0 = (V_A/1000 Ohms) - (0.03 A)

Solving for V_A, we get:

V_A = (0.03 A)(1000 Ohms) = 30 Volts

Now, we can use this value for V_A to find the power absorbed by element X. The power absorbed by a resistive element can be calculated using the equation P = V^2/R, where P is power in watts, V is voltage in volts, and R is resistance in ohms. In this case, we have:

P = (30 V)^2 / 4000 Ohms = 0.225 Watts

Therefore, the power absorbed by element X is 0.225 Watts. I would also suggest practicing more problems using KCL to improve your understanding and accuracy in solving these types of problems.