power最佳解釋40分

Two bulbs rated 200V,60W and 200,100W respectively are connected first in parallel and then in series to a 200V a.c. mains supply
assuming temperature no change.
Which of the following correct describes the relative brightness of the lamps?
*************In parallel**********In series
A.*******60W is brighter*****60W is brighter
B.*******60W is brighter*****100W is brighter
C.*****100W is brighter******60W is brighter
D.*****100W is brighter*****100W is brighter

答案是C。
和AC或DC無關。

200V，60W燈泡的電阻為
R = V2/P = 2002/60 = 667Ω
200V，100W燈泡的電阻為
R = V2/P = 2002/100 = 400Ω
所以可知100W的燈泡它的內阻較小。

電器的功率可以用下式考慮
P = I2R 及
P = V2/R
由兩式中，一個功率和電阻成正比，一個和電阻成反比。但應該是用什麼考慮。
這個問題和電路的串聯並聯的性質有關。
並聯電路電壓相同。串聯電路電流相同。

並聯時因為電壓相同，所以用 P=V2/R，由於電壓相同，它的功率便可電阻成反比，所以100W的電阻較小。所以並聯時，100W燈泡會較光。
串聯時因為電流相同，所以便用P=I2R來考慮，它的電阻愈大，功率便愈大。所以在串聯時，60W的燈泡便較光。

若另一方面考慮，一般家庭中的電路，是用並聯的電路，自然地，在並聯的時候，功率愈大(100W)光度愈大。

在串聯的電路，因為兩者的電流相同，依V=IR，所以在串聯電路中，電阻大的部份電壓愈大，電壓愈大，主要能量便會在這部份釋出。例如使用電爐時，電線是和電爐的發熱絲串聯，發熱絲的電阻較大，所以發熱絲便會放出較多能量。60W和100W的燈泡，60W的電阻較大，所這部份的電壓較大，因此愈會較光。

Let B1 is 200V, 60W;
and B2 is 200V, 100W.

Let resistance of B1 is R1=V^2/P = 200^2/60 ~= 666 Ohm
and resistance of B2 is R2=V^2/P = 200^2/100 = 400 Ohm

Assume the ratio of their ability to transfer electricity into heat and light are similar, this assumption is just to prevent higher rating bulb give more heat but less light than lower rating bulb as it is abnormal and affect the correct answer. (but i think no need to consider too deep on this... only a MC question)

When they connected in parallel, the p.d. between both the 2 bulbs are 200V so B2 is brighter because B2 transfer more power into light.

When they connected in series, the current flow through them is constant, so B1 transfer more power into light because R1 is greater than R2 and P=I^2R.

So the answer is C.

ac or dc is no difference because there are only resistance in this question, no capacitor or inductor.

二燈泡評價200 V，60 W 和200，100 W 分別把第1 並聯連接然後連續到一200 V a.c. 供電幹線
沒有假定溫度為變化。
下列coorectl中的哪個描述燈的有關的亮度？
*************並聯 **********連續
A。 *******60 W更明亮 *****60 W更明亮
B。 *******60 W更明亮 *****100 W更明亮
C。 *****100 W更明亮 ******60 W更明亮
D。 *****100 W更明亮 *****100 W更明亮