Hey everyone, I am having trouble understanding the following question (answer i

Question

Hey everyone,

I am having trouble understanding the following question (answer isprovided below). Could someone please explain why that's theanswer? Help would be greatly appreciated. Thanks! -A

Question: A light bulb and a coil of conducting wire are connectedin series to a voltage source
consisting of a
A) 12 V battery
B) 12 Vrms transformer, operating at 60 Hz frequency (as inthe USA)
C) 12 Vrms transformer, operating at 50 Hz frequency (as inEurope)
The order of bulb brightness (greatest first), when connected toeach of these sources, is

Answer: ACB

Explanation / Answer

   1.   Brightness of bulbdepends upon current through it, more current means morebrightness.    2.   Current depends uponimpedance (Z) of bulb,          I   =   V/ Z       which depends uponresistance (R) and reactance of coil (XL) as          Z   =   (R2   +   XL2)          Since Ris a constant,    Z varies as XL,greater is XL , greater is Z.    3.   Finally, XL (and hence Z) depends upon frequency, as          XL   =   * L   =   2 * f * L          greateris frequency, more is Z    a.   Now forDC.   f   =   0,   hence   XL   =   0,   Z   =   R          Idc   =   V/R    b.   for AC at 60Hz,   XL   =   2* 3.14 * 60 * L   =   376.8 *L   =>   Z   =   (R2   +   (376.8*L)2)    c.   for AC at 50Hz,   XL   =   2* 3.14 * 50 * L   =   314 *L   =>   Z   =   (R2   +   (314* L)2)          Clearly       Idc   >   I50   >   I60       i.e.   ACBis correct sequence.       i.e.   ACBis correct sequence.

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