nicekikah

2021-08-15

The current in a wire varies with time according to the relation

How many coulombs of charge pass a cross section of the wire in the time interval between

Express your answer using two significant figures.

What constant current would transport the same charge in the same time interval?

Express your answer using two significant figures.

Cristiano Sears

Skilled2021-08-16Added 96 answers

Step 1

The charge passing through a cross section in the time interval is given by

$q={\int}_{{t}_{1}}^{{t}_{2}}Itd$

Substitute$(55A-\left(0.65\frac{A}{{s}^{2}}\right){t}^{2})$ for I, 0s for $t}_{1$ , and 8.5s for $t}_{2$ to find the charge.

$q={\int}_{0s}^{8.5s}(55A-\left(0.65\frac{A}{{s}^{2}}\right){t}^{2})dt$

$={\left[55tA\right]}_{0s}^{8.5s}-{\left[\frac{0.65{t}^{3}}{2}\right]}_{0s}^{8.5s}$

$=467.5C-133.1C$

$=334.1C$

The amount of charge that pass a cross section in the given time interval is 334.1C.

Step 2

The constant current is given by the equation

$I=\frac{Q}{\mathrm{\u25b3}t}$

$=\frac{Q}{{t}_{2}-{t}_{1}}$

Substitute 334.1 C for Q and 8.5s for$t}_{2$ and 0s for $t}_{1$ to find I.

$I=\frac{334.1C}{8.5s-0s}$

$=39.3A$ .

The constant current that would transport the charge is 39.3A.

Answer:

The amount of charge that pass a cross section in the given time interval is 334.1C.

The constant current that would transport the charge is 39.3A.

The charge passing through a cross section in the time interval is given by

Substitute

The amount of charge that pass a cross section in the given time interval is 334.1C.

Step 2

The constant current is given by the equation

Substitute 334.1 C for Q and 8.5s for

The constant current that would transport the charge is 39.3A.

Answer:

The amount of charge that pass a cross section in the given time interval is 334.1C.

The constant current that would transport the charge is 39.3A.

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