Total power of resistors in a circuit

In summary, the conversation involves calculating the total power of resistors in a circuit and discusses the use of Thevenin equivalents and formulas for calculating power when given voltage or current. The initial attempt at a solution includes some errors, including an incorrect value for Thevenin Resistance and missing opportunities to directly calculate powers. The correct voltage values for R2, R3, and R4 are provided and the correct formula for calculating power is mentioned.
  • #1
doktorwho
181
6

Homework Statement


In this problem we are asked to calculate the total power of the resistors in the circuit below.
First.JPG

Homework Equations



##P=I^2R##

The Attempt at a Solution


My solution goes like this:
PT=PR1+PR2+PR3+PR4+PR5
I can find PR1 and PR5 immediately from the given current generators:
PR1=IG1^2*R1
PR5=IG2^2*R5
Second.JPG

Since i know those powers one i don't need the current generators and can transform the right and left sides to thevenin equivalents:
Clearly
ET1=-ET2
ET1=E1=24V and RT1=R1=12Ω (i hope i got this right)
Third.JPG

Forth.JPG

Now we can see that we have this type of situation. I transformed the resistor 3 as in the picture and can divide the circuits into 2 and the powers of the resistors will the sum of two.
Fifth.JPG

I will be solving the left one:
Re=R3R2/(R3+R2)=4Ω
I=ET1/(Re+R1) = 24/18 = 4/3 A
and the power of two element are P3'+P2=Re*(4/3)^2 and that times 2 is the total power.
Something is wrong here. The result should yield 312 W and i just don't get that. What is wrong?
 
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  • #2
PR1 and PR5 are correct.

Now, what are the voltages across R2, R3 and R4 ? ( Forget about Thevenin and so on )
 
  • #3
I'm not liking your Thevenin equivalents. In particular, I don't like the Thevenin Resistance value. What happens when you suppress both sources in the sub-circuit that you're converting?

I also think you're missing out on further opportunities to directly calculate powers in certain resistors. You should have a formula for power when you know the voltage across a resistor, as well as one for when you know the current through it.
 
  • #4
Oh, how dumb of me. I have the voltage across R2 and R4 and it's 24V for the R2 and -24 for the R4 so the voltage across R3 is -48V right? If so the formula is ##P=\frac{U^2}{R}##
 
  • #5
Hesch said:
PR1 and PR5 are correct.

Now, what are the voltages across R2, R3 and R4 ? ( Forget about Thevenin and so on )

gneill said:
I'm not liking your Thevenin equivalents. In particular, I don't like the Thevenin Resistance value. What happens when you suppress both sources in the sub-circuit that you're converting?

I also think you're missing out on further opportunities to directly calculate powers in certain resistors. You should have a formula for power when you know the voltage across a resistor, as well as one for when you know the current through it.
Is the above corrrect?
 
  • #6
doktorwho said:
Oh, how dumb of me. I have the voltage across R2 and R4 and it's 24V for the R2 and -24 for the R4 so the voltage across R3 is -48V right? If so the formula is ##P=\frac{U^2}{R}##
Right.
 
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Related to Total power of resistors in a circuit

1. What is the formula for calculating the total power of resistors in a circuit?

The formula for calculating the total power of resistors in a circuit is P = VI, where P is power in watts, V is voltage in volts, and I is current in amperes.

2. How do you calculate the total resistance of a circuit?

To calculate the total resistance of a circuit, you would add up the individual resistances of all the resistors in the circuit. If the resistors are in series, you would simply add them together. If they are in parallel, you would use the formula 1/R = 1/R1 + 1/R2 + 1/R3 + ..., where R is the total resistance and R1, R2, R3, etc. are the individual resistances.

3. What is the relationship between power and resistance in a circuit?

The relationship between power and resistance in a circuit is inversely proportional. This means that as resistance increases, power decreases, and vice versa. This is because a higher resistance in a circuit will result in a lower current, which in turn decreases the amount of power being used.

4. How does the total power of resistors in a circuit affect the overall performance?

The total power of resistors in a circuit can affect the overall performance in a few ways. First, a higher total power can cause the circuit to overheat, which can lead to malfunctions or damage. Additionally, a higher power consumption can result in higher energy costs. On the other hand, a lower total power can result in a weaker or slower performance of the circuit.

5. What factors can affect the total power of resistors in a circuit?

The total power of resistors in a circuit can be affected by several factors, including the individual resistor values, the circuit's voltage and current, the type of circuit (series or parallel), and any external factors such as temperature or humidity. Additionally, the use of different materials for the resistors can also affect the total power in a circuit.

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