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 = VPVP = 240 V

Voltage of the secondary = VSVS = 12 V

Power of secondary = PSPS = 30 W


To Find:


Current in primary= IPIP = 30 W


Solution:


For an ideal transformer, we know that 

Power Input = Power Out

As P = VII So,

VPVP IPIP = VsVs IsIs 

or

IPIP = VsIsVPVsIsVP  ------(1)

but the value of IsIs is also unknown so, we have for the secondary coil

PSPS = VSVS ISIS 

Or

IsIs = PSVSPSVS

Thus equation (1) after putting the relation of  IsIs

IPIP = Vs(PSVs)VP


IP = PSVP


Now putting all the corresponding values in equation (1)

IP = 30W240V

IP = 0.125 A ----------------Ans. 1

----------------------------------------------

Now for the transformation ratio, we know that

NSNP = VSVP

By putting values 

NSNP = 12V240V

NSNP = 120 ------------Ans. 2



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