How Do You Calculate Power Absorbed by a Resistor in a Circuit?

In summary: Good job!In summary, the problem involved determining the power absorbed by a 15 ohms resistor in a circuit. The approach involved using KCL and KVL laws, as well as Ohm's law, to calculate the current in each branch. However, the answer key provided was incorrect due to a miscalculation.
  • #1
homo-sapiens
28
0

Homework Statement


Determine the power absorbed by the 15 ohms resistor, see circuit below.(the ix, i1, and i2 are things i added)
http://puu.sh/bQyEk/5f47888b03.png

2. Homework Equations
the KCL law
the KVL law
the ohm's law
power = voltage * current

The Attempt at a Solution


I calculated the whole resistance of the second branch first. then I found the relationship between current ix and current i since the voltage of a loop = zero. I then calculated the current using the KCL current law. i then found a relationship between current i1 and current i2. I calculated current i2 and used the power = resistance * current * current.
My answer is way off from the answer key, and I would like to know what I did wrong??

http://puu.sh/bQyK1/715544a6a1.png
 
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  • #2
Your approach looks good. It looks like you miscalculated ix = 36/51*(.425).
 
  • #3
ops! that was a minor mistake on my part, but the answer is still not right with the answer key...
here is the answer key
http://puu.sh/bQDw6/e03756b3b0.jpg
 
Last edited by a moderator:
  • #4
The answer key is wrong. It comes up with v = -19 when solving for -2 - 2*v/6 = v/8.5 + v/6 + v/6, which is clearly incorrect (I calculate v = -2.55).
 
  • #5
OH! thank you so much for clearing this up for me. aw, never thought the answer key would be wrong. I guess I should believe in my methods more often. thank you again.
 
  • #6
You're welcome! It's always unnerving when the answer key is wrong, but it's nice when you can spot the mistake so you know for sure.
 

1. What is a basic circuit and how does it work?

A basic circuit is a complete and closed path through which electricity can flow. It consists of a power source, such as a battery, wires to carry the current, and a load, such as a light bulb, that uses the electricity. When the circuit is closed, the power source pushes the electrons through the wires, and the load converts the electrical energy into some other form, such as light or heat.

2. What is Ohm's Law and how is it used in circuits?

Ohm's Law is a fundamental principle in electricity that describes the relationship between voltage, current, and resistance in a circuit. It states that the current flowing through a conductor is directly proportional to the voltage and inversely proportional to the resistance. In circuits, Ohm's Law is used to calculate the amount of current that will flow through a circuit when a certain voltage is applied, or to determine the resistance needed to limit the current to a desired level.

3. How do you calculate the total resistance in a series circuit?

In a series circuit, the total resistance is the sum of all the individual resistances. This can be calculated using the formula Rtotal = R1 + R2 + ... + Rn, where R1, R2, etc. are the resistances of each component in the circuit. This means that in a series circuit, the total resistance is always greater than the resistance of any individual component.

4. What is the difference between series and parallel circuits?

In a series circuit, all components are connected in a single loop, so the current is the same at every point in the circuit. In a parallel circuit, the components are connected in branches, so the current is divided between the branches. Additionally, in a series circuit, the total resistance is the sum of all the individual resistances, whereas in a parallel circuit, the total resistance is less than the resistance of any individual branch.

5. How does the resistance of a wire affect the flow of current?

The resistance of a wire affects the flow of current by limiting the amount of current that can flow through it. A wire with higher resistance will allow less current to flow through it than a wire with lower resistance. This is because the higher resistance wire will require more voltage to push the same amount of current through it, according to Ohm's Law. In practical terms, a higher resistance wire will result in a dimmer light or less heat produced by a circuit.

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