Thermal energy/ heat in a parallel connection

[AnneX]

Homework Statement:

Nope, I am studying for a quiz

Relevant Equations:

Not sure, but R and W could be directly proportional...

In a parallel connection heat is produced.

R1 = 5 Ohm

R2 = 10 Ohm

What is the relation of W1/W2?



1:4

1:2

2:1

1:8

3:1

I’d tend to say 1:2, but I am not really sure…

 

[Merlin3189]

Whats the formula for W? (When you know R and you know something else because they are in parallel.)

 

[AnneX]

The current flowing through R1 is double the current flowing through R2

 

[Merlin3189]

Do you know any formula for the heat generated W in a resistance R when a current I flows and there is a pd of V across it?

 

[Merlin3189]

Or, actually, you've <nearly> solved it with your correct answer $I_1 = 2 I_2$

Edited in <>

 

[Merlin3189]

Do you know
Power=Voltage x Current $W=VI$
Voltage = Current x Resistance $V=IR$
So $W= VI \ = \ IR I \ = \ I^2R$
or $I = \frac{V}{R}$
So $W= VI \ = \ V \frac{V}{R} \ = \ \frac{V^2}{R}$

 

[AnneX]

So, it is 2:1?

 

[Merlin3189]

Yes.
You can always put some numbers in, as you do here, but the formulae are useful to remember.

Important thing here is, to know that the voltage is the same across both, when they in parallel.
So P=IV tells you that power is proportional to current. Current 2:1 so power 2:1

If they were in series, the current would be the same. If you work out the voltages,
P=IV tells you the power is proportional to the voltage for the same current.

 

[AnneX]

Thanks for the help 👍
One more question though, if the two resistors were in series would it be W1 : W2 = 1:2

 

[cnh1995]

One more question though, if the two resistors were in series would it be W1 : W2 = 1:2

Yes.