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Trigonometric Methods, using instantaneous value of current

  • Thread starter rikiki
  • Start date
  • #1
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Homework Statement



The instantaneous value of current, i amp, at t seconds is given by:

i = 15 sin(100π.t + 0.6)

Find the value of;
a) amplitude
b) period
c) frequency
d) initial phase angel
e) value of i when t = 2.5s
f) time when current first reaches maximum value

Homework Equations



i=A*sin(ωτ+∅)

i = A.sin(2pi.f.t + ∅)

The Attempt at a Solution



I understand from looking around these are the correct formula to use, is someone please able to explain how to arrive at the formula from question statement i = 15 sin(100π.t + 0.6)? having some difficulties understanding the math involved. Thanks.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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compare the formulas one has a 15 and the general formula has an A for amplitude so now you have the first answer

next do a comparison with the omega *t + theta term inside the sin function and match with the actual formula that should answer you other parts.

for initial phase angle consider the case when t=0

This problem is pretty straightforward and is just trying to get you to extract the facts from the formula so review the A * sin (omega *t + theta) formula to understand each parameter.

also you need to show some work before we can help.
 
  • #3
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Thanks for your prompt reply, that makes the application of the formula very clear. I'm still struggling to find any literature on where the actual 'general' formula comes from. I don't know if your able to help at all with this? my notes on this seem pretty sparce and can't seem to find anything much on the web. Is there anywhere you can think of that will explain this in a bit more detail. Thanks for your help.
 
  • #5
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Perfect. Thanks very much. I'll get going on the answers. Thanks for your help, much appreciated.
 
  • #6
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answers to date, i'd be grateful if anybody is able to check they're ok.


2 a) Current=maximum amplitude ×sin (Angular frequency ×time+phase angle)
I_((t) )=Im ×sin⁡(ωt+ θ)
I_((t) )=15 ×〖sin 〗⁡(100πt+ 0.6)
∴ Amplitude = 15
Angular frequency=100π rad/s
Phase angle=0.6 radians

2 b) Period= 2π/(angular frequency)
T= 2π/ω
T= 2π/100π
T= 6.2831853071796/314.1592653589793
P= 0.02s


2 c) Angular frequency=2 × π ×f
ω=2.π.f
100π=2.π.f
314.1592653589793= 6.2831853071796 ×f
f= 314.1592653589793/6.2831853071796
f= 49.9999999999999
f=50Hz



2 d) Phase angle=0.6 radians or 34º
deg⁡〖=rad .180/π〗
deg⁡〖=0.6 × 180/π〗
deg⁡〖=0.6 × 57.2957795130823 〗
deg⁡〖= 34.3774677078494 〗
deg⁡〖=34º〗

2 e) i=15sin⁡(100πt+0.6)
i=15sin⁡(100π2.5+0.6)
i=15 sin⁡(785.9981633974483)
i= 13.7029862899072
i=13.7amps

2 f) I_((t) )=Im ×sin⁡(ωt+ θ)
I_((t) )=15 ×sin⁡(100π.t+ 0.6)
I_((t) )=15 ×sin⁡(314.1592653589793 × t + 0.6)


I'm having a few difficulties trying to find an equation to calculate t. Is there a way of using the phase relationship between voltage and current or is there a more mathematical way of calculating this? i've read about creating a derivative of the function? my maths is pretty poor, so if anyone could offer some here that would be much appreciated. Thanks.

I'm not sure if i've had a mare and need to recalculate some of my answers with my calculator in the radians setting?
 
  • #7
answers to date, i'd be grateful if anybody is able to check they're ok.

2 e) i=15sin⁡(100πt+0.6)
i=15sin⁡(100π2.5+0.6)
i=15 sin⁡(785.9981633974483)
i= 13.7029862899072
i=13.7amps

2 f) I_((t) )=Im ×sin⁡(ωt+ θ)
I_((t) )=15 ×sin⁡(100π.t+ 0.6)
I_((t) )=15 ×sin⁡(314.1592653589793 × t + 0.6)


I'm having a few difficulties trying to find an equation to calculate t. Is there a way of using the phase relationship between voltage and current or is there a more mathematical way of calculating this? i've read about creating a derivative of the function? my maths is pretty poor, so if anyone could offer some here that would be much appreciated. Thanks.

I'm not sure if i've had a mare and need to recalculate some of my answers with my calculator in the radians setting?

Hi,

I think from 2e onwards you need your calculator in the radians setting. This would give you an answer for when t=2.5 of 8.47amps.
Could someone confirm my suspicions?
 

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