In Europe, the standard voltage is 230 V (rms), AC, and 50 cycles/s. Suppose you
ID: 1426330 • Letter: I
Question
In Europe, the standard voltage is 230 V (rms), AC, and 50 cycles/s. Suppose you take your 8.00 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? i(rms, USA) . A i(rms, Rome)A
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.) Yes / No
(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. Np Ns
(d) What is the resistance of your razor? .
Explanation / Answer
a)
Power rating = P = 8 W
rms Voltage in america = V' = 120 volts
using the formula
P = V'2 /R
8 = 1202 / R
R = 1800 ohm
In Rome , V = 230 volts
so power drawn = P' = V2/R = 230 x 230 / 1800 = 29.4 watt
b)
In Us ,
rms current = rms Voltage / resistance = Vrms/R = 120 / 1800 = 0.067 A
In Rome ,
rms current = rms Voltage / resistance = Vrms/R = 230 / 1800 = 0.128 A
Yes
c)
Vr = Voltage in rome = 230
Va = Voltage in US = 120
Np / Ns = Vr / Va = 230 / 120 = 1.92
d)
Power rating = P = 8 W
rms Voltage in america = V' = 120 volts
using the formula
P = V'2 /R
8 = 1202 / R
R = 1800 ohm