Power dissipated in circuit combination

In summary, the resistors R1, R2, and R3 are connected to a battery and the power dissipated by each is represented by p1, p2, and p3 respectively. To find the relationship between p1 and p2, the total resistance in the circuit is first determined by combining R2 and R3 in parallel and then adding this equivalent resistance to R1 in series. This allows for finding the total current in the circuit, which is then used to calculate the power dissipated by R1. By labeling the current through R2 as I and using Kirchhoff's law, it can be shown that p2 = 1/9 * p1. Additionally, for extra credit, the ratio of p
  • #1
alex21
6
0

Homework Statement



three resistors R1=R2 and R2=2R3, are connected to a battery, as show in the figure, if the power dissipated for each one is p1,p2 and p3 respectirvely;p3 must be equal to:

Homework Equations



P=VI
P=V^2/R
P=I^2*R

The Attempt at a Solution



I have tried to find the total resistance in the circuit by knowing that R2 and R3 are in parallalel and this equivalent resistance let's call it R23 will be in series with R1 so the equivalent resistance would be Req=R1+R23 this will allow me to find the total current in the circuit which is I=V/Req while doing so I should be able to find the power in R1 with this P=I^2*R1 since the total current in the circuit is the same going through R1, but I can't find the relationship with the power dissipated with P2 and as you can see P1 is in terms of P2
 

Attachments

  • Sin título-1.jpg
    Sin título-1.jpg
    14.8 KB · Views: 1,266
Physics news on Phys.org
  • #2
Your third Relevant Equation is important. The question wants you to express the power dissipated by R1 in terms of the power dissipated by R2. So aim towards expressing R1 in terms of R2 and the current through R1 in terms of the current through R2. KCL and the current division rule will come in handy :wink:
 
  • #3
alex21 said:

Homework Statement



three resistors R1=R2 and R2=2R3, are connected to a battery, as show in the figure, if the power dissipated for each one is p1,p2 and p3 respectirvely;p3 must be equal to:

Homework Equations



P=VI
P=V^2/R
P=I^2*R

The Attempt at a Solution



I have tried to find the total resistance in the circuit by knowing that R2 and R3 are in parallalel and this equivalent resistance let's call it R23 will be in series with R1 so the equivalent resistance would be Req=R1+R23 this will allow me to find the total current in the circuit which is I=V/Req while doing so I should be able to find the power in R1 with this P=I^2*R1 since the total current in the circuit is the same going through R1, but I can't find the relationship with the power dissipated with P2 and as you can see P1 is in terms of P2

Welcome to the PF.

Hint -- a simpler approach would be to assign values to the resistors (like 1 Ohm and 2 Ohms), and then look at how current divides between R2 and R3. Label the current through R2 = I. Then what is the current through R3? And what does that mean the current is through R1?

And solve...Please show us your work toward the solution! :smile:
 
  • #4
lets call i the total current in the circuit therefore the current that goes through R1. applying kirchhoff's law to the junction where R2 and R3 splits i=i1+i2 the total current is the sum of the current that goes through R2 and R3
so we have:
i=i1+i2
i=V/R2 + V/R3
i=(R3+R2)V/R2*R3
but R2=2R3
i=(R3+2R3)V/R2*R3
i=3V/R2

I will assume V is the voltage drop on R2 so
V=iR2/3
And the power dissipated P2=V^2/R2 and P1=I^2*R1 so we have
P2=(iR2/3)^2/R2
P2=i^2R2^2/9R2
P2=i^2R2/9
but R1=R2 and P1=I^2*R1
P2=1P1/9
P1=9P2
 
  • #5
Correct! :smile:
 
  • #6
berkeman said:
Correct! :smile:

it would make any sense to ask P3?
 
  • #7
alex21 said:
it would make any sense to ask P3?

For extra credit? Sure!

What is P1/P3?
 

1. What is power dissipation?

Power dissipation is the process by which energy is converted into heat within a circuit. This occurs when current flows through a resistance, causing a voltage drop and generating heat as a result.

2. How is power dissipation calculated?

Power dissipation is calculated using the formula P = I^2 * R, where P is power in watts, I is current in amps, and R is resistance in ohms. In some cases, this formula can also be represented as P = V^2 / R, where V is voltage in volts.

3. How does power dissipation affect electronic components?

Excessive power dissipation can cause electronic components to overheat, leading to malfunctions or even permanent damage. It is important to properly calculate and manage power dissipation in circuits to ensure safe and efficient operation of electronic devices.

4. What factors can affect power dissipation in a circuit?

The main factors that affect power dissipation in a circuit are current, resistance, and voltage. Other factors such as temperature, component material, and circuit design can also play a role in determining power dissipation.

5. How can power dissipation be reduced in a circuit?

Power dissipation can be reduced in a circuit by using components with lower resistance, limiting the current flowing through the circuit, or reducing the voltage applied to the circuit. Proper heat management, such as using heat sinks or fans, can also help to reduce power dissipation in circuits.

Similar threads

Engineering Solve Superposition Theorem for R1, R2 Circuit
    • Engineering and Comp Sci Homework Help
Replies
18
Views
2K
How should I Approach this Circuit Calculation?
    • Engineering and Comp Sci Homework Help
Replies
7
Views
906
Engineering Calculating the voltage at a certain Resistor
    • Engineering and Comp Sci Homework Help
Replies
3
Views
820
How to find the equivalent resistance of this electric circuit?
    • Engineering and Comp Sci Homework Help
Replies
5
Views
3K
Power dissipated by a resistor in combined citcuit
    • Engineering and Comp Sci Homework Help
Replies
4
Views
2K
Engineering Current Amplification Circuit
    • Engineering and Comp Sci Homework Help
Replies
12
Views
1K
Calculating the voltage in an OP-amp circuit with a current source
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Comp Sci Need help finding the resistor size for a circuit (Ohm's law)
    • Engineering and Comp Sci Homework Help
Replies
1
Views
936
Engineering Find the unknown resistance in this series circuit
    • Engineering and Comp Sci Homework Help
Replies
7
Views
3K
Engineering Circuit input impedance with ground in an OP Amp circuit
    • Engineering and Comp Sci Homework Help
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top