Question

A sinusoidal voltage is zero att=(−2π/3)msand increasing at a rate of80,000 V/s. The maximum amplitude of the voltage is80 V. What is the frequency ofvin radians per second? Express your answer in radians per second to three significant figures.

Answer 1

To find the frequency of the sinusoidal voltage, we need to convert the given frequency from hertz to radians per second. The angular frequency can be found by setting the derivative of the voltage function equal to the given rate of change in voltage and solving for ω.

Step-by-step explanation:

To find the frequency of the sinusoidal voltage in radians per second, we need to convert the given frequency from hertz to radians per second. In a sinusoidal function, the frequency is given by the formula f = ω/2π, where f is the frequency in hertz and ω is the angular frequency in radians per second.

Given that the maximum amplitude of the voltage is 80 V, we can determine the angular frequency using the formula V = Vosin(ωt), where V is the voltage at time t, Vo is the peak voltage, and ω is the angular frequency in radians per second.

Since the voltage is increasing at a rate of 80,000 V/s, we know that the derivative of the voltage function with respect to time is 80,000 V/s. Taking the derivative of the voltage function V = 80sin(ωt), we get dV/dt = 80ωcos(ωt). Setting this derivative equal to 80,000 V/s and solving for ω, we can find the angular frequency.