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Byju's Answer
Standard XII
Physics
Kirchhoff's Junction Law
If current ...
Question
If current
I
1
=
3
A
s
i
n
ω
t
and
I
2
=
4
A
c
o
s
ω
t
, then
I
3
is
A
5
A
s
i
n
(
ω
t
+
53
∘
)
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B
5
A
s
i
n
(
ω
t
+
37
∘
)
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C
5
A
s
i
n
(
ω
t
+
45
∘
)
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D
5
A
s
i
n
(
ω
t
+
30
∘
)
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Solution
The correct option is
C
5
A
s
i
n
(
ω
t
+
53
∘
)
I
1
=
3
A
sin
ω
t
I
2
=
4
A
cos
ω
t
as from kirchoff's law
I
3
=
I
1
+
I
2
I
2
=
3
A
sin
ω
t
+
4
A
cos
ω
t
Multiplying and dividing the RHS with
√
(
3
A
)
2
+
(
4
A
)
2
=
5
A
I
2
=
5
A
(
3
5
sin
ω
t
+
4
5
cos
ω
t
)
as
cos
53
0
=
3
5
sin
53
0
=
4
5
⇒
I
3
=
5
A
(
cos
53
0
sin
ω
t
+
sin
53
0
cot
ω
t
)
I
2
=
5
A
sin
(
cot
+
53
0
)
as
sin
(
A
+
B
)
=
sin
A
cos
B
+
cos
A
sin
B
I
3
=
5
A
sin
(
ω
t
+
53
0
)
Suggest Corrections
1
Similar questions
Q.
If
I
1
=
π
/
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∫
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I
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Q.
If current
I
1
=
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A
sin
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t
and
I
2
=
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A
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t
, then
I
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is :
Q.
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2009
(
t
a
n
x
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2009
d
x
a
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d
I
3
=
∫
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2010
(
t
a
n
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Q.
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t
h
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