AC Frequency: Calculating from V, I, & t

[arod2812]

Homework Statement

A light bulb is connected to a 120.0-V wall socket. The current in the bulb depends on the time t according to the relation I = (0.669 A) sin [(491 Hz)t].

What is the frequency of the alternating current?

Homework Equations

How do I use the given value for I?? (since it includes time, t)

The Attempt at a Solution

I know that V=Vo * sin2pi * freq * time

 

[mezarashi]

The only relevant equation you should be using is:

sin(kt)

Suppose I have the equation sin(pi*x), can you tell me what the period of this function is? Can you tell me the frequency? Draw it out. Now if I tell you I have the equation sin(491*x), can you tell me the same information?

You will notice a pattern such as: sin(k*x) -> sin(2*pi*f*x) in terms of frequency.

 

[Moetasim]

To calculate the frequency, we can use the equation V=IR, where V is the voltage, I is the current, and R is the resistance of the circuit. In this case, we can rearrange the equation to solve for frequency: f=V/(IR).

Since we are given the voltage (120.0 V) and the current equation (I = (0.669 A) sin [(491 Hz)t]), we can plug in these values to solve for frequency.

f= (120.0 V)/[(0.669 A) sin [(491 Hz)t] * R]

The resistance of the circuit is not given in the problem, so we cannot solve for frequency with this method.

Alternatively, we can use the formula for AC frequency: f=1/T, where T is the period of the current. We can find the period by taking the inverse of the frequency, so T=1/491 Hz.

Therefore, the frequency of the alternating current is 491 Hz.