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Mathematics
Mathematics
Problem
Over a
10
s
10\text{ s}
10
s
interval, two electric currents
I
1
(
t
)
I_1(t)
I
1
(
t
)
and
I
2
(
t
)
I_2(t)
I
2
(
t
)
flow through a circuit. It is known that
∫
0
10
I
1
(
t
)
d
t
=
12
C
\displaystyle\int_{0}^{10} I_1(t)\,dt = 12\text{ C}
∫
0
10
I
1
(
t
)
d
t
=
12
C
and
∫
0
10
I
2
(
t
)
d
t
=
−
4
C
\displaystyle\int_{0}^{10} I_2(t)\,dt = -4\text{ C}
∫
0
10
I
2
(
t
)
d
t
=
−
4
C
. The net charge transferred during the interval is defined as
Q
=
∫
0
10
(
I
1
(
t
)
+
0.5
I
2
(
t
)
)
d
t
Q=\displaystyle\int_{0}^{10}\bigl(I_1(t)+0.5\,I_2(t)\bigr)\,dt
Q
=
∫
0
10
(
I
1
(
t
)
+
0.5
I
2
(
t
)
)
d
t
. Determine
Q
Q
Q
.
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