Question

The rechargeable batteries for a laptop computer need a much smaller voltage than what a wall socket provides. Therefore, a transformer is plugged into the wall socket and produces the necessary voltage for charging the batteries. The batteries are rated at 9.0 V, and a current of 187 mA is used to charge them. The wall socket provides a voltage of 120 V. (a) Determine the turns ratio of the transformer. (b) What is the current coming from the wall socket? (c) Find the average power delivered by the wall socket and the average power sent to the batteries.

Answer 1

In transformers we know that

Np/Ns = Vp/Vs = is/ip

Np = number of turns in primary transformer

Ns = number of turns in secondary transformer

Vp = 120 V

Vs = 9.0 V, So

Np/Ns = Vp/Vs

Here it's not given that in which ratio is required (Np/Ns) OR (Ns/Np), check both and let me know which one works.

Np/Ns = 120/9 = 13.33

OR

Ns/Np = 9/120 = 0.075 (Try this one first)

Part B.

Vp/Vs = is/ip

Vp = 120 V & ip = ?

Vs = 9.0 V & is = 187 mA = 0.187 A

So,

ip = is*(Vs/Vp)

ip = 0.187*(9.0/120) = 0.014 Amp = 14 mA

Part C.

Power delivered by the wall socket will be:

Pp = ip*Vp = 120*0.014 = 1.68 W

Power sent to batteries will be

Ps = is*Vs = 9.0*0.187 = 1.68 W

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