Question 128: Current Electricity

Question

Current passing through a wire as function of time is given as $I(t)=0.02 t+0.01 \mathrm{~A}$. The charge that will flow through the wire from $t=1 \mathrm{~s}$ to $t=2 \mathrm{~s}$ is

Accepted Answer

To find the total charge $ q $ that flows through the wire from $ t = 1 \, 	ext{s} $ to $ t = 2 \, 	ext{s} $, we can integrate the current function $ I(t) = 0.02t + 0.01 \, 	ext{A} $ over this interval.
The formula for the charge $ q $ flowing through the wire is given by the integral of the current with respect to time:
$ q = \int I(t) \, dt $
We integrate the function from $ t = 1 $ to $ t = 2 $:
$ q = \int_1^2 (0.02t + 0.01) \, dt $
To solve this, first find the antiderivative:
$ q = \left[ 0.02 \frac{t^2}{2} + 0.01t ight]_1^2 $
Calculate the expression at the upper and lower bounds:
$ = \left[ 0.01t^2 + 0.01t ight]_1^2 $
Plug in the values:
For $ t = 2 $:
$ = 0.01(2)^2 + 0.01(2) = 0.04 + 0.02 = 0.06 $
For $ t = 1 $:
$ = 0.01(1)^2 + 0.01(1) = 0.01 + 0.01 = 0.02 $
Subtract the result at $ t=1 $ from the result at $ t=2 $:
$ q = 0.06 - 0.02 = 0.04 \, 	ext{C} $
Therefore, the charge that flows through the wire from $ t = 1 \, 	ext{s} $ to $ t = 2 \, 	ext{s} $ is $ 0.04 \, 	ext{C} $.

Answer

0.02 C

Answer

0.07 C

Answer

0.06 C

Answer

0.04 C

Current Electricity

Current passing through a wire as function of time is given as I(t)=0.02 t+0.01 \mathrm{~A}. The charge that will flow through the wire from t=1 \mathrm{~s} to t=2 \mathrm{~s} is

Choose the correct answer: