An ideal step-down transformer is connected to the main supply of 240 V. It is desired to operate a 12 V, 30 W lamp. Find the current in the primary and the transformation ratio? (Ans: 0.125 A, 1/20).
Data Given:
Voltage of the Primary = VP = 240 V
Voltage of the secondary = VS = 12 V
Power of secondary = PS = 30 W
To Find:
Current in primary= IP = 30 W
Solution:
For an ideal transformer, we know that
Power Input = Power Out
As P = VI So,
VP IP = Vs Is
or
IP = VsIsVP ------(1)
but the value of Is is also unknown so, we have for the secondary coil
PS = VS IS
Or
Is = PSVS
Thus equation (1) after putting the relation of Is
IP = Vs(PSVs)VP
IP = PSVP
Now putting all the corresponding values in equation (1)
IP = 30W240V
IP = 0.125 A ----------------Ans. 1
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Now for the transformation ratio, we know that
NSNP = VSVP
By putting values
NSNP = 12V240V
NSNP = 120 ------------Ans. 2
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