The charge passing through a conductor increases over time as q = 2.0t3 + 7.7 wh

Question

The charge passing through a conductor increases over time as q = 2.0t3 + 7.7 where t is in seconds.

(a) What equation describes the current in the circuit as a function of time?

(b) What is the current in the conductor at t = 0.0 s and at t = 1.0 s?

In a television set phosphorescent materials of different colors on the face of the picture tube glow when they are hit by a beam of electrons that scans rapidly across the face of the tube. If the beam current in a particular TV is 50µA and the charge on a single electron is 1.6X10-19 C how many electrons hit the face of the picture tube in one second?

Explanation / Answer

A: current I = dq/dt

I = d(2t^3 + 7.7) /dt

I = 6t^2 + 0

so

current eqn is 6t^2

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at t = 0 , current i0 = 0 A

at t = 1 , current I1 = 6 * 1^2 = 6 Amps

------------------------------------

Current i = charge /time

i = Q/t

but charge Q = ne

so

curent i = ne/t

n = i t /e

n = 50 *10^-6 * 1/(1.6 *10^-19 )

n = 3.12 *10^14 electrons

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