Up next in 10
The current, I in an a. c circuit is given by the equation: I = 30sin100πt, where t is the time
1K views
Dec 3, 2024
The current, I in an a. c circuit is given by the equation: I = 30sin100πt, where t is the time in seconds.
View Video Transcript
0:01
the
0:02
current the current I in an AC circuit
0:08
is given by the
0:10
equation I = 30 sin 1005
0:16
T where
0:18
T is in seconds reduce the
0:23
following from this
0:26
equation number one frequency of the
0:30
current pi value of the current and the
0:34
root me squ of the current to find the
0:39
frequency of the current the first thing
0:42
we need to do is to uh deduct is to
0:45
deduct our
0:46
data and to do that we will now say that
0:51
since we have this
0:53
equation
0:54
I is equal
0:57
to 30
1:02
s
1:07
100
1:10
100
1:11
5 we now equate it with I
1:17
not is equals
1:20
to or will not say sorry I isal to
1:27
i s
1:31
2 5 f
1:35
t so this is what we have we are now
1:38
equating I
1:40
=
1:45
30 as I = I sin 2
1:50
F
1:52
this
1:54
party corresponds with I
1:57
not and if we do that you to find the
2:03
frequency we will now say that this
2:08
uh
2:11
1005 this
2:13
10050 corresponds with
2:16
[Music]
2:20
2 25
2:24
F corresponds with 25 F
2:28
so5 Cor responds with 25
2:32
ft 30 corresponds with I so
2:37
now to solve question one we now say
2:41
that the frequency is equal to
2:46
100 5
2:49
T is equal
2:51
to now we have 25 ft we now write
2:57
25 ft
3:00
Pi will cancel
3:02
Pi T will cancel T and we be left
3:08
with will be left with
3:15
100 is equals
3:17
to this is 100 is equals to we have two
3:21
here 2
3:24
F and dividing both sides by two we now
3:28
have
3:30
this will cancel this 2 into 2 1 2 into
3:35
100 is 50 therefore our frequency f is
3:41
equal to
3:43
50
3:45
HZ let's go to equation two question two
3:49
sorry find the F
3:51
value find the P value of the current to
3:56
find the P value of the current we will
3:58
now say that
4:00
I
4:02
here I not here is the P value I
4:06
corresponds to 30 therefore I which is
4:10
the P value is equal to
4:14
30 therefore we
4:18
now use the unit of I I not which is in
4:24
amp therefore 30
4:26
amp the third question find the square
4:30
of the
4:31
current three to find the root me square
4:35
of the current the first thing we need
4:37
to do is to remember that
4:44
i²
4:45
isal I which is the F current all over <
4:51
tk2 and this is going to give us I note
4:54
here is 30 therefore we have 30 over <
4:58
tk2
5:00
now if we use sord form we now have
5:06
30 < tk2 * <
5:10
tk2 over < tk2 the reason why I said 22
5:16
remember
5:18
that 1 / 1 is = 1 2 / 1 = 2 and 2 / 2 =
5:29
1
5:30
therefore if I sayun
5:34
2k2 is also the same thing as 1 and if I
5:39
now say x * <
5:43
tk2
5:45
over <
5:48
tk2 is the same thing as x
5:53
* one and this is the same thing as X
5:57
therefore we are now applying this same
6:00
method here this is the same thing as
6:03
now if we multiply here we now going to
6:05
have
6:07
30 < tk2 30 byun2 and < tk2 byun2 will
6:11
give
6:13
us <
6:14
TK4 and this is the same thing as 30 <
6:20
tk2 all over sare root of 4 is going to
6:24
give us 2 and 2 into 2 1 2 into 30 will
6:29
give give us 15 and this is going to
6:34
be
6:36
15 <
6:39
tk2 therefore we have our iot me
6:43
squ
6:45
IUN mean
6:48
squ is equal to 15 < tk2
6:53
aamp remember that anair is the unit of
7:00
current but in this case we can now
7:04
still said okay what is RO
7:08
true if we change it into we can now
7:12
still write it as I square is equal to
7:18
21
7:21
point is equal to
7:25
21.
7:26
21 ere ere there and this is the
7:32
final answer
#Mathematics
#Physics