In Europe, the standard voltage is 230 V (rms), AC, and 50 cycles/s. Suppose you take your 5.00 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?
Ω
PLEASE SHOW ALL WORK AND EQUATIONS AND INDICATE FINAL ANSWERS!!!
a. P = E^2/R = (120)^2/R = 5.00 W.,
R = (120)^2/5 = 2,880 Ohms.
P = (230)^2/2880 = 18.4 W.
b. U.S.A.: 120I = 5.0, I = 0.0417A.
Rome: 230I = 18.4, I = 0.08A.
I = 1.2 * 0.0417 = 0.050A = Current at which the razor will be damaged. Yes.
c. Np/Ns = Vp/Vs = 230/120 = 1.92/1.
d. R = 2880 Ohms(See part a).
To find the answers to these questions, we need to use the relationship between power, voltage, and current: P = IV, where P is power, I is current, and V is voltage.
(a) To find the power the razor will draw in Rome, we can use the equation P = IV. The voltage in Rome is 230 V, and the power of the razor is given as 5.00 W. So, we can rearrange the equation to solve for the current: I = P/V.
I = 5.00 W / 230 V = 0.0217 A
Therefore, the power drawn by the razor in Rome would be 5.00 W.
(b) In the United States, the voltage is 120 V. Using the same equation, we can solve for the current:
I = 5.00 W / 120 V = 0.0417 A
Therefore, the rms current that will run through the razor in the United States is 0.0417 A.
In Rome, the current would be the same as calculated in part (a), which is 0.0217 A.
(c) To use the razor in Rome without damaging it, we need a transformer that can convert the voltage from 230 V to 120 V. Transformers can step up or step down the voltage depending on the ratio of the number of windings in the primary coil (Np) to the secondary coil (Ns). To get a voltage conversion from 230 V to 120 V, we need a step-down transformer.
The ratio of winding for a step-down transformer is given as Np/Ns = Vp/Vs, where Vp is the primary voltage and Vs is the secondary voltage.
Substituting the given values, we have:
Np/Ns = 230 V / 120 V = 1.92
Therefore, we would need a step-down transformer with a ratio of 1.92:1 (approximately).
(d) To find the resistance of the razor, we can rearrange the equation P = IV to get R = V/I.
We know that in Rome, the voltage is 230 V and the current is 0.0217 A (as calculated in part (a)).
R = 230 V / 0.0217 A ≈ 10596 Ω
Therefore, the resistance of the razor is approximately 10596 Ω.
To summarize the answers:
(a) The power drawn by the razor in Rome is 5.00 W.
(b) The rms current in the United States is 0.0417 A, and in Rome, it is 0.0217 A.
(c) To use the razor in Rome without damaging it, a step-down transformer with a ratio of 1.92:1 would be needed.
(d) The resistance of the razor is approximately 10596 Ω.