SOLUTION: use proportions to solve a transformer reduces or increases the voltage (V) of an alternating current based on the ratio of the coils in the input circuit (N in) to the coils in

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Question 991290: use proportions to solve
a transformer reduces or increases the voltage (V) of an alternating current based on the ratio of the coils in the input circuit (N in) to the coils in the output circuit (N out) according to the following proportion: V out/ V in = N out/ N in. A transformer is used to reduce the 120V household current to the 18V used in model train sets. If the transformer has 180 coils on the input circuit, how many coils are on the output circuit?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
V_in= 120V, V_out = 18V, N_in = 180 coils, N_out = x coils.

A proportion:

18%2F120 = x%2F180,

The solution:

x = %2818%2A180%29%2F120 = %2818%2A3%29%2F2 = 9*3 = 27 coils.


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
VO / VI = NO / NI

VO = voltage out
VI = voltage in
NO = number of coils out
NI = number of coils in

VI = 120 volts
VO = 18 volts

NI = 180
NO = x

x = the number of coils out.

you want to solve for x.

VO / VI = NO / NI becomes 18 / 120 = x / 180

cross multiply to get 18 * 180 = 120 * x

divide both sides of the equation by 120 to get 18 * 180 / 120 = x

solve for x to get x = 27.

number of coils out needs to be equal to 27.

you get:

VI = 120
VO = 18
NI = 180
NO = 27

VO / VI = NO / NI becomes 18 / 120 = 27 / 180

simplify to get .15 = .15 which is true, confirming the solution is correct.

the solution is that the number of coils on the output circuit are equal to 27.