Question

In a US household, the voltage in an electric outlet (in volts) is given by the following equation, where t is in seconds. V = 156sin(120 pi t) However, in a European house, the voltage is given (in the same units) by the following equation. V = 339sin(100 pi t) Answer the following questions comparing the voltages in the two regions.
How much greater is the maximum voltage in a European house than a US house? ________ volts
What is the number of cycles (oscillations) per second in a US house? ________ cycles/second

Answer 1

Answer:

a) The voltage in an european house is 2,17 times greater than in an american House. That is 183 volts more than in US.

b) the number of cycles or oscillations for an US House is 60 cycles per second

Explanation:

To answer this this question you have to know the wave equation:

x(t) = A Sin (a + b.t)

where

x(t) = is the position as a time function... In this exercise we could call V(t) instead of x(t) beacause we want to know voltage vs time.

A = is the amplitude of the wave. In this case the maximum voltage that can be reached.

a = is the offset in time or number of waves (zero in this exercise)

b =  constant that varies the frequency

then...

a) calculate the ratio between both amplitudes:

$A_{Europe} / A_{US} = 339 / 156 = 2,17$

b) frequency (Oscillations) is:

b = 2pi/T = 2pi*F    remember that: T = 1/F

where

F = frequency

T = Period

so for US household we have:

120pi =2pi*F

therefore

F = 120/2 = 60 Hertz