# AC circuit, voltage and frequency problem

## Homework Statement

According to Equation 20.7, an ac voltage V is given as a function of time t by V = Vo sin 2
ft
, where Vo is the peak voltage and f is the frequency (in hertz). For a frequency of 64.7 Hz, what is the smallest value of the time at which the voltage equals one-half of the peak-value?

## Homework Equations

V = Vo sin2(3.14)ft

## The Attempt at a Solution

1/2Vo = Vo sin(2*3.14*64.7*t)

I know I set this equation wrong with the 1/2Vo but I don't understand how to do that part, the answer I got this way is .0738 V

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You need to know the angle ## \theta ## that has ##\sin(\theta)=\frac{1}{2} ##. And here, with this voltage function as a function of time, we are working in radians, so you need to write that angle ## \theta ## in radians. ## \\ ## For starters, you need to know the angle in degrees that has ## \sin(\theta)=\frac{1}{2} ##, and then convert that angle to radians.

haruspex
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I know I set this equation wrong
Looks right to me.
the answer I got this way is .0738 V

You need to know the angle ## \theta ## that has ##\sin(\theta)=\frac{1}{2} ##. And here, with this voltage function as a function of time, we are working in radians, so you need to write that angle ## \theta ## in radians. ## \\ ## For starters, you need to know the angle in degrees that has ## \sin(\theta)=\frac{1}{2} ##, and then convert that angle to radians.
How do you know its in radians?

You need to know the angle ## \theta ## that has ##\sin(\theta)=\frac{1}{2} ##. And here, with this voltage function as a function of time, we are working in radians, so you need to write that angle ## \theta ## in radians. ## \\ ## For starters, you need to know the angle in degrees that has ## \sin(\theta)=\frac{1}{2} ##, and then convert that angle to radians.
Never mind, I angular velocity=2pif

haruspex
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How do you know its in radians?
At this level, radians would be standard as input to a trig function. A calculator would generally assume radians unless you tell it otherwise.
In the present case, you have to assume that in the given sin(2
ft)
the 2
ft
part is in radians. The presence of the "

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Looks right to me.

*Vo cancel out*
1/2= sin(406.5t)
1/2= sin(.523599)
t=406.5/.523599 = .0012880664 s

haruspex
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*Vo cancel out*
1/2= sin(406.5t)
1/2= sin(.523599)
t=406.5/.523599 = .0012880664 s
Correct, but don't quote so many digits. The frequency is only specified to three sig figs.

I entered .001 s and I still have it wrong

I got it, the answer was supposed to be in scientific notation