Power Dissipated for 2 different circuits

AI Thread Summary
To determine the ratio of R1 to R2 for equal power dissipation in circuits A and B, the currents through R2 must be set equal, leading to the equation (2EMF)/(2R1+R2) = (EMF)/[(R1^2/2R1) + R2]. The discussion highlights uncertainty about simplifying the equation by removing EMF, which is indeed constant. For part B, the condition under which power dissipated in circuit A exceeds that in circuit B is debated, with R2 > R1 being a proposed solution. Participants express confusion regarding calculations and seek confirmation on their findings, particularly when substituting values for R2.
lowcard2
Messages
8
Reaction score
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
 
Physics news on Phys.org
Diagram please.
 
totally forgot but here it is

4km5h.jpg
 
deleting my post
 
if i can take out EMF and make R2 = 1 i come out with 4 as my answer. can anyone confirm?
 
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Thread 'Trying to understand the logic behind adding vectors with an angle between them'
My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
Back
Top