Calculating Total Power of Heaters Connected in Series

[figs]

One heater uses 339.40 W of power when connected by itself to a battery. Another heater uses 231.45 W of power when connected by itself to the same battery. How much total power do the heaters use when they are both connected in series across the battery?

I tried to work with P=VI with the two wattages given, but i wasnt sure
where to go from there.

 

[Sirus]

A deceptive title!

Power is additive in series circuits.

$$P_{total}=P_{1}+P_{2}+P_{3}+...+P_{n}$$

 

[vincentchan]

Power is additive in series circuits.

$$P_{total}=P_{1}+P_{2}+P_{3}+...+P_{n}$$

NO, they do not.....

you can set the battery has a voltage $V$
calculate the resistant for each heater in term of $V$

then use

$$R_{total} = R_{1} + R_{2}$$

to find the total resistant in series... after you have the total resistant, you can get the total current, finally, use your P=VI

if everything is right, you will get something like $$\frac{1}{P_{total}} = \frac{1}{P_{1}} + \frac{1}{P_{2}}$$

 

[dextercioby]

VINCENTCHAN,WHAT ARE U TALKING ABOUT...?

$$P=UI=R_{equiv}I^{2}$$

$$U_{1}=R_{1}I$$

$$U_{2}=R_{2}I$$

$$U=U_{1}+U_{2}$$

$$R_{equiv}=R_{1}+R_{2}$$

$$P_{1}=U_{1}I$$

$$P_{2}=U_{2}I$$

$$P=UI=(R_{1}I+R_{2}I)I=P_{1}+P_{2}$$

Daniel.

 

[vincentchan]

DEXTERCIOBY: WHAT DID YOU TALKING ABOUT
assume the battery has a fixed voltage instead of fixed current (which is most of the case)

$$P_{1} = V^2/R_{1}$$
$$P_{2} = V^2/R_{1}$$
$$R_{1} = V^2/ P_{1}$$
$$R_{2} = V^2/ P_{2}\\$$

$$R_{total} = R_{1}+R_{1}= V^2/ P_{1}+V^2/ P_{2}$$

$$P_{total} =V^2/R_{total} = \frac{V^2}{ V^2/ P_{1}+V^2/ P_{2}}$$

$$= \frac{1}{1/P_{1} + 1/P_{2}}$$

PS
dextercioby,
please tell me how do you make those large letter as you did in other thread... I can't figure it out myself...

edit:
ha ha, i figure it out now

YOU ARE SO WRONG, DEXTERCIOBY

 

[Chris]

Aren't dextercioby and vincentchan answering different questions?
Dextercioby gives the proof that the total power output for a given series circuit is the sum of the power outputs from all the components in that series circuit.
Vincentchan addresses what I believe was the original question. The initial data is the power output when each component is the only component in the circuit. When the two components are put into the same circuit, vincentchan's formula holds true.
P1 and P2 are defined differently in the conflicting posts, so they are both correct, imo.
Chris

 

[dextercioby]

Yes,you're are right...My analysis,though principially correct,didn't take into account the data of the problem (the fact that it is the same battery and the P_{1} & P_{2} don't have the significance i thought they would...).

Daniel.

P.S.Which letters are you talking about...?


EDIT:In your dreams,Vincentchan... :tongue2: