Question

A sinusoidal voltage v (t) has an rms value of 30 V , a period of 120 μs , and reaches a positive peak at t = 30 μs . Assume v(t) = Vmcos(ωt+θ).

a) Determine the peak voltage Vm.
b) Determine the frequency f.
c) Determine the phase corresponding to a time interval of t = 30 μs .

Answer 1

a) The peak voltage is 42.43 V. b) The frequency is 8.33 MHz. c) The phase corresponding to a time interval of t = 30 μs is -1.88 radians.

Step-by-step explanation:

a) To determine the peak voltage, we can use the formula Vm = √2 * Vrms. Given that the rms value is 30 V, we can substitute it into the formula:
Vm = √2 * Vrms = √2 * 30 V = 42.43 V

b) To determine the frequency, we can use the formula f = 1 / T, where T is the period. Given that the period is 120 μs, we can substitute it into the formula:
f = 1 / T = 1 / (120 × 10^-6 s) = 8.33 MHz

c) To determine the phase corresponding to a time interval of t = 30 μs, we can use the formula θ = -ωt. Given that ω is the angular frequency and is equal to 2πf, we can substitute the values and calculate the phase:
θ = -ωt = -(2πf)(30 × 10^-6 s) = -2π(8.33 × 10^6 s^-1)(30 × 10^-6 s) = -1.88 radians