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

I=55A-(0.65As2)t2. (a) How many coulombs of charge pass a cross section of the wire in

the time interval between t=0and role="math" localid="1655721302619" t=8.0s? (b) What constant current would transport the

same charge in the same time interval?

Short Answer

Expert verified

a) The charge passing through the wire between 0-8 seconds is 329 C

b) The constant current that would transport this charge is 41.0A

Step by step solution

01

Write the formula of current.

Consider the formula for the current:

I=Qt

Here, Q is the charge and t is the time.

02

Calculation of charge passing between 0-8 seconds.

(a)

Consider the relation for the time and the current is:

I=55A-0.65As2t2

Apply the formula for the current to determine the charge.

Q=55-0.65t2dtQ=0855-0.65t2dtQ=55t-130.65t308Q=440-111

Solve further as,

Q=329C

03

Calculation of the constant current in the wire.

(b)

Solve for the current in the wire.

I=QtI=330C8sI=41.0A

Therefore, the value of the current is 41.0 A .

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