In Europe, the standard voltage is 230 V (rms), AC, and 50 cycles/s. Suppose you

Question

In Europe, the standard voltage is 230 V (rms), AC, and 50 cycles/s. Suppose you take your 6.00 W electric razor to Rome and plug it into the receptacle (with an adapter to fit the receptacle but not to change the voltage). (The standard voltage in the United States is 120 V (rms), AC, and 60 cycles/s.)

(a) What power will it draw in Rome?
W

(b) What rms current will run through the razor in the United States and in Rome?

Is the razor in danger of being damaged by using it in Rome without a voltage adapter? (Assume the razor will be damaged if it carries a current 20% larger than its standard operating current in the United States.)

YesNo    

(c) If you want to use the razor in Rome without damaging it, what type of transformer would you need? Express your answer as a ratio between the number of winding in the primary coil in comparison to the secondary coil.

=  

(d) What is the resistance of your razor?

Explanation / Answer

Here,

Vrms = 230 V

f = 50 Hz

power , P = 6 W

a)

let the resistance is R

R = V^2/Power

R = 120^2/6

R = 2400 Ohm

power draw in Rome = 230^2/2400

power draw in Rome = 22.04 W

the power draw in Rome is 22.04 W

b)

Using Ohm's law

I(rms , USA) = Vrms/R

I(rms , USA) = 120/(2400)

I(rms , USA) = 0.05 A

---------

I(rms,Rome) = Vrms/R

I(rms,Rome) = 230/2400

I(rms,Rome) = 0.0958 A

c)

for the transformer in Rome

Vp = 230 V

Vs = 120 V

Np/Ns = Vp/Vs

Np/Ns = 230/120

Np/Ns = 1.917

d)

as found above

the resistance of razor is 2400 Ohm

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