The primary windings of a transformer which has an 88% efficiency are connected

Question

The primary windings of a transformer which has an 88% efficiency are connected to 220-V ac. The secondary windings are connected across a 2.6-, 75-W lightbulb.

Part A
Calculate the current through the primary windings of the transformer.Express your answer using two significant figures and include the appropriate units.

Part B
Calculate the ratio of the number of primary windings of the transformer to the number of secondary windings of the transformer.Express your answer using two significant figures.

Explanation / Answer

Given that,

efficiency e = 0.88

Vp = 220 V

R = 2.6 ohm

Ps = 75 W

(A)

Let power in primary winding = Pp

Current = lp

Here, Ps = 0.88*Pp

Ps = 0.88*lp*Vp

lp = 75 / 0.88*220

lp = 0.387 A

(B)

Ps = Vs^2 / R

Vs = sqrt (Ps*R)

ratio of the number of primary windings to the number of secondary windings,

Np / Ns = Vp / Vs

Np / Ns = Vp / sqrt(Ps*R) = 220 / sqrt (75*2.6)

Np / Ns = 15.75

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