# AC Frequency: Calculating from V, I, & t

• arod2812
In summary, the current in a light bulb connected to a 120.0-V wall socket can be represented by the equation I = (0.669 A) sin [(491 Hz)t]. The frequency of the alternating current is 491 Hz. To use the given value for current, the relevant equation to use is sin(kt), where k represents the frequency. For example, if the equation is sin(pi*x), the frequency is pi and if the equation is sin(491*x), the frequency is 491. This follows the pattern of sin(k*x) -> sin(2*pi*f*x) in terms of frequency.
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

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.

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.

## 1. What is AC frequency?

AC frequency refers to the number of complete cycles of alternating current (AC) that occur in one second. It is measured in Hertz (Hz) and determines the rate at which the direction of the current changes.

## 2. How do you calculate AC frequency?

The formula for calculating AC frequency is f = 1/T, where f is the frequency in Hz and T is the period in seconds. The period can be determined by measuring the time it takes for one complete cycle of the AC waveform. Alternatively, it can be calculated by dividing the total time (t) by the number of cycles (n), so T = t/n.

## 3. Can AC frequency be calculated from voltage, current, and time?

Yes, AC frequency can be calculated from voltage (V), current (I), and time (t) using the formula f = VI/2π. This formula is derived from the relationship between frequency, voltage, current, and resistance in an AC circuit.

## 4. What is the difference between AC frequency and AC power frequency?

AC frequency refers to the rate of change of direction of the current in an AC circuit, while AC power frequency refers to the frequency of the voltage supplied by the power source. In most countries, the standard AC power frequency is 50 or 60 Hz, depending on the power grid system.

## 5. Why is it important to calculate AC frequency?

Calculating AC frequency is important for understanding and analyzing AC circuits. It can help in troubleshooting electrical issues, designing and optimizing circuits, and ensuring the proper functioning of electrical equipment. AC frequency is also crucial in determining the compatibility of different electrical components and devices.

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