Power Dissipated for 2 different circuits

In summary, the question asked for the ratio of R1 and R2 where the power dissipated by the resistor of resistance R2 is the same for both circuit A and circuit B. The equations used were P = IV = I^2 x R = V^2/R. To find the ratio, the two equations for the current for R2 in each circuit were set equal to each other and simplified. For part B, the most restrictive answer for when the power dissipated by the resistance in circuit A is bigger than that of circuit B is R2>R1. This was determined by plugging in numbers and simplifying the equations.
  • #1
lowcard2
8
0
Part A:
For what ratio of R1 and R2 would power dissipated by the resistor of resistance R2 be the same for circuit A and circuit B?

current for R2 of circuit A is (2EMF)/(2R1+R2)
current for R2 of circuit B is (EMF)/[(R1^2/2R1) + R2)

Part B:
Under which of the following conditions would power dissipated by the resistance in circuit A be bigger than that of circuit B? Choose the most restrictive answer.
R2<R1
R2>R1
R2<2R1
R2<.5R1

Equations used:
P = IV = I^2 x R = V^2 /R

Attempt:
I understand since R and P is same for both i only have to make the 2 currents equal.
(2EMF)/(2R1+R2) = (EMF)/[(R1^2/2R1) + R2)
I haven't taken physics or math class in 2 years so I'm kinda unsure on how to continue.
Since EMF is constant can I just remove it?

For part B just by plugging in numbers R2>R1 works but I am not certain
 
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  • #2
Diagram please.
 
  • #3
totally forgot but here it is

4km5h.jpg
 
  • #4
deleting my post
 
  • #5
if i can take out EMF and make R2 = 1 i come out with 4 as my answer. can anyone confirm?
 

Related to Power Dissipated for 2 different circuits

What is power dissipation?

Power dissipation is the rate at which energy is converted from one form to another within an electrical circuit. It is typically measured in watts (W) and represents the amount of energy that is lost or converted into heat within the circuit.

How is power dissipation calculated?

Power dissipation can be calculated by multiplying the voltage across a circuit by the current flowing through it. This is known as Joule's law and is represented by the equation P = VI, where P is power, V is voltage, and I is current.

What factors affect power dissipation?

The main factors that affect power dissipation in a circuit include the voltage, current, and resistance. Higher voltages and currents will result in higher power dissipation, while lower resistance will lead to lower power dissipation.

What is the difference between power dissipation in series and parallel circuits?

In a series circuit, the total power dissipation is distributed evenly among the components, while in a parallel circuit, each component has its own individual power dissipation. This means that the total power dissipation in a parallel circuit is higher than in a series circuit.

Why is power dissipation important to consider in circuit design?

Power dissipation is important to consider in circuit design because it can affect the efficiency and performance of the circuit. Excessive power dissipation can lead to overheating and damage to components, while insufficient power dissipation can result in a circuit not functioning properly.

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