SOLUTION: three batteries are connected in series so that the total voltage is 54. the voltage of the first battery is twive the voltage of the second and 1/3 the voltage of the thrird batt

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Question 200423: three batteries are connected in series so that the total voltage is 54. the voltage of the first battery is twive the voltage of the second and 1/3 the voltage of the thrird battery. find the actual voltage of each battery
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Working Eqn:
B%5B1%5D%2BB%5B2%5D%2BB%5B3%5D=54v

Conditions:

The voltage of 1st battery is twice the 2nd:
B%5B1%5D=2B%5B2%5D ---> %281%2F2%29B%5B1%5D=B%5B2%5D, A

The 1st battery is 1/3 of the 3rd:
B%5B1%5D=%281%2F3%29B%5B3%5D -----> 3B%5B1%5D=B%5B3%5D, B

Subst. A & B in Working Eqn:
B%5B1%5D%2Bhighlight%28%281%2F2%29B%5B1%5D%29%2Bhighlight%283B%5B1%5D%29=54v
4.5B%5B1%5D=54v
cross%284.5%29B%5B1%5D%2Fcross%284.5%29=cross%2854%2912v%2Fcross%284.5%29
red%28B%5B1%5D=12v%29

Via conditions:
12v=2B%5B2%5D ---> B%5B2%5D=12%2F2
red%28B%5B2%5D=6v%29

12v=%281%2F3%29B%5B3%5D ---> B%5B3%5D=12%2A3
red%28B%5B3%5D=36v%29

Check,
12v%2B6v%2B36v=54v
54v=54v

Thank you,
Jojo