Find V_0 in the circuit (6 elements)

In summary, the problem involves using conservation of energy to solve for V_0. The total power is calculated by adding the individual powers (p_1, p_2, etc.). After simplifying, the equation becomes 3V_0 = 54W, resulting in V_0 = 18V. The only error is that V_0 should have units of volts, not watts. The rest of the problem is correct.
  • #1
VinnyCee
489
0
http://img68.imageshack.us/img68/51/problem120ha2.jpg

Use conservation of energy to solve for [itex]V_0[/itex].

[tex]P_1\,=\,(30V)\,(-6A)\,=\,-180W[/tex]
[tex]P_2\,=\,(12V)\,(6A)\,=\,72W[/tex]
[tex]P_3\,=\,(V_0)\,(3A)\,=\,(3V_0)W[/tex]
[tex]P_4\,=\,(28V)\,(2A)\,=\,56W[/tex]
[tex]P_5\,=\,(28V)\,(1A)\,=\,28W[/tex]
[tex]P_6\,=\,(10V)\,(-3A)\,=\,-30W[/tex]

[tex]\sum\,p\,=\,p_1\,+\,p_2\,+\,p_3\,+\,p_4\,+\,p_5\,+\,p_6[/tex]

[tex]\sum\,p\,=\,(-180W)\,+\,(72W)\,+\,[(3V_0)W]\,+\,(56W)\,+\,(28W)\,+\,(-30W)[/tex]

[tex]3V_0\,=\,54W[/tex]

[tex]V_0\,=\,18\,V[/tex]

Does this look right?
 
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  • #2
Looks okay until the last step (units).

EDIT -- BTW, this belongs in the homework forums, not the general forums.
 
  • #3
Do you mean the summation of the p's? I don't see a unit error, could you point it out please:)

I didn't see the "Engineering" Forum over at Homework help section, but now I found it, thanks for the heads up!
 
  • #4
VinnyCee said:
Do you mean the summation of the p's? I don't see a unit error, could you point it out please:)
Vo should not have units of watts. Just a small typo.
 
  • #5
OIC, thank you!

[itex]V_0[/itex] should have units of Volts!

Other than that, the problem looks OK?

I will post other problems in the homework section, thanks for the help!
 
  • #6
it is right if you are taking (3v) as a combination volt*amp. as previously u have takev 3*vo as power. so it looks right to me.
 

Related to Find V_0 in the circuit (6 elements)

1. How do I find the value of V_0 in this circuit?

To find the value of V_0 in a circuit with 6 elements, you will need to use Kirchhoff's voltage law (KVL) and Ohm's law. First, apply KVL to create a loop by starting at one point in the circuit and following the path of the circuit back to that point. Then, use Ohm's law to calculate the voltage drop across each element in the loop. Finally, add all of the voltage drops together and set it equal to zero. Solve for V_0 to find its value.

2. What is Kirchhoff's voltage law (KVL)?

Kirchhoff's voltage law states that the sum of all the voltage drops in a closed circuit is equal to the sum of all the voltage rises in the same circuit. This means that the sum of the voltage drops across each element in a circuit must equal the voltage supplied by the voltage source.

3. How do I apply Kirchhoff's voltage law (KVL) in a circuit with 6 elements?

To apply KVL in a circuit with 6 elements, start at one point in the circuit and follow the path of the circuit back to that point, creating a loop. Then, use Ohm's law to calculate the voltage drop across each element in the loop. Finally, add all of the voltage drops together and set it equal to zero. This will allow you to solve for the value of V_0.

4. What is Ohm's law?

Ohm's law states that the voltage drop (V) across a resistor is equal to the product of the current (I) through the resistor and the resistance (R) of the resistor. This can be represented by the equation V=IR. It is a fundamental law in circuit analysis and can be used to calculate the voltage drop across any resistor in a circuit.

5. How can I use Ohm's law to find the voltage drop across each element in a circuit with 6 elements?

To use Ohm's law to find the voltage drop across each element in a circuit with 6 elements, you will need to know the current through each element and the resistance of each element. Then, use the equation V=IR to calculate the voltage drop across each element. This information can then be used in conjunction with Kirchhoff's voltage law (KVL) to find the value of V_0 in the circuit.

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