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IF AN A•C IS REPRESENTED BY I= IoSinwt. CALCULATE THE INSTANTANEOUS VALUE OF SUCH A CURRENT
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Jan 23, 2025
IF AN A•C IS REPRESENTED BY I= IoSinwt. CALCULATE THE INSTANTANEOUS VALUE OF SUCH A CURRENT, IF IN A CIRCUIT IT HAS A RIMS VALUE OF 15•OA WHEN ITS PHASE ANGLE IS 30° (WAEC 1989)
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if an AC is represented by I = I sin
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Omega T calculate the instantaneous
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value of such a current if in a circuit
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it has a root me Square value of 15.0
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aere when it space angle is
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30°
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now we we will first extract our data
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which is step one if an AC cycle is
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represented by this calculate the
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instantaneous value of such a
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current if in a circuit it
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has a root S value of
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15.0 a
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therefore
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I root means
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square is equal to 15.0
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I'm
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fair when it is face angle is
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30° the face
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angle
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this Omega T represents Theta therefore
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this this is the face angle therefore
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the face angle is Theta which is Omega T
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which
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is
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30° the face angle is 30°
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which
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is
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30° if an AC is represented by this
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equation calculate the instantaneous
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value of such a current the
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instantaneous value of such a
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current
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I is equal
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to
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I sin
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Omega T this is the formula we going to
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use however we don't know the value of I
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not therefore we supposed to
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use we go back to our
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data and say that we're looking for
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I and then we also looking for I
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remember that I not is the fake current
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and I is the instantaneous value
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of such a
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current so we are looking for two things
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here therefore to find I
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not we will say we use this equation
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which
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is <
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tk2
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*
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IUN
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me
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squ now we'll first start by using this
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equation and then we use this
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equation
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Now using I
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not equals
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to < tk2 square root of two
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here square root of 2 * IUN squ IUN
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Square here isal 15 therefore we say
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time
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15 therefore I not
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is equal to < TK 2 * 15 when you use
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your calculator you're going to have uh
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21.
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21
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next therefore IAL which is the current
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is
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21.2 next we're going to use this
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formula i = i t therefore to find
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instant continuous current we say this
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is equal to I not I not here is
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2121 then we say therefore we will say
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21
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21
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* s of Omega T this is going to be S of
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30° and therefore this is going to give
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us 21
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2. 21 * s of 30° is is going to be
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0.5
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therefore I is equal to when you use
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your calculator again you see that I =
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21.1 *
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0.5 is going to give
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you let me press my
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calculator it's going to give you
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10.61 aamp therefore you're going to
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have
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10.61 which is your instant
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instantaneous current therefore as you
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can see this is the
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solution I Square = 15 from our data we
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had i² = 15.0
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Aleta = to Omega T which is 30° I not
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was not given to us I which is the
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instantaneous current therefore we use
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the formula I = I Omega T which was
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already given to us from the question
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therefore now since we don't have I not
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we need to use a formula which says I
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notal to 2 * IUN
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squ therefore since I Square was given
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to us which is 15
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now we multip it by uh root of two and
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we got 21.2 one which is a f current and
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this is I not now we use I in page two
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from Fage two as you can
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see I = to
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2121 which is the F current we
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substituted the value of oh we instead
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of writing I not we now set 2 2121
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Time s of 30° 30° is the face angle as
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you can see from our data therefore s of
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30° = 0.5 therefore 0.5 * 21.2 will give
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you 10.61 a which is the instantaneous
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current
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as therefore this is the final answer
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