v(t) = 12 sin(913t + 71°) volts. Find (a) angular frequency in radians per second, (b) frequency in Hz, (c) period, (d) maximum voltage, (e) minimum voltage, (f) Peak-to-Peak voltage , (g) rms voltage, (h) average voltage, (i) voltage expressed as a phasor, (j) the average power consumed by a 220 ohm resistor having this voltage , and (k) the voltage at t= 3ms

Explanation:

v(t) = 12 sin(913t + 71°) volts

a )  913° = (π / 180) x  913 radians

= 15.92 radians

a ) angular frequency  ω = 15.92 radians / s

b ) ω = 2πn

n = ω / 2π

= 15.92 / 2 x 3.14

= 2.53 Hz

c ) Period = 1 / n

= 1 / 2.53 = .4 s .

d )

Maximum voltage = 12 volt

e) Minimum volts = - 12 volts

g  ) rms volts = V / √2

= 12 / √2

= 8.48 V

h )

Average voltage = 0

j ) Average power

Vrms² / R

= 12 x 12 / 2 x 220

= .327 W.

k )

v(t) = 12 sin(913t + 71°)

v(t) = 12 sin(913x .003 + 71°)

=  12 sin(73.7°)

= 11.5 V .

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.

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