Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Which mathematical expression gives the total charge
Δ
q
\Delta q
Δ
q
that passes through a wire during the time interval from
t
=
0
t=0
t
=
0
to
t
=
T
t=T
t
=
T
when the current varies with time as
I
(
t
)
I(t)
I
(
t
)
? a)
Δ
q
=
T
I
(
0
)
\displaystyle \Delta q = T\,I(0)
Δ
q
=
T
I
(
0
)
b)
Δ
q
=
I
(
0
)
+
I
(
T
)
2
T
\displaystyle \Delta q = \dfrac{I(0)+I(T)}{2}\,T
Δ
q
=
2
I
(
0
)
+
I
(
T
)
T
c)
Δ
q
=
∫
0
T
I
(
t
)
d
t
\displaystyle \Delta q = \int_{0}^{T} I(t)\,dt
Δ
q
=
∫
0
T
I
(
t
)
d
t
d)
Δ
q
=
∫
0
T
t
d
I
d
t
d
t
\displaystyle \Delta q = \int_{0}^{T} t\,\dfrac{dI}{dt}\,dt
Δ
q
=
∫
0
T
t
d
t
d
I
d
t
Browse the problem library