00:01Hi friends, what you sow is what you reap.
00:05Therefore, if you start learning, you will reap commensurate results.
00:11A DC voltage source can produce a regular electric current according to a mathematical equation.
00:19Now, we are asked to calculate how much electric charge flows through a cable for seconds after the DC voltage
00:25source is turned on.
00:28You can see the mathematical equation for electric current in the problem sheet.
00:35As usual, this is a simplified view of the conducting wire inside the cable.
00:42The circle in the center represents the cross-sectional area of the inspection area.
00:49When viewed from the front, the circle looks like a straight vertical line.
00:57Electric current flows from left to right.
01:00This means electrons will flow from right to left.
01:05Note the arrangement of electrons through the cross-sectional area.
01:10The number of electrons is unique for each time.
01:14The number of electrons is determined by the mathematical equation.
01:21By definition, electric current is the change in electric charge per unit time.
01:27I equals dq dt.
01:31From here, dq equals i dt.
01:36From the problem sheet, the electric current is 1.2t plus 2.5 amperes.
01:44d is not a number, it is a derivative operator.
01:51To obtain the derivative value, we must perform an integration process.
01:56Simply integrate both sides from the initial condition to the final condition.
02:01Initially, the voltage source is not yet on, and at time t equals 0 seconds, q equals 0.
02:08And the final condition is t equals 4 seconds.
02:14You may not have learned integration math in the first semester.
02:18The integral of a x to the power n with respect to x is a over n plus 1, times
02:24x to the power n plus 1.
02:27A is the coefficient of x.
02:32Consider this formula for a moment.
02:39Returning to our problem, the integral of 1 with respect to q is q.
02:45The integral of 1.2t with respect to t is 0.6t squared.
02:53The integral of 2.5 with respect to t is 2.5t.
03:00Now, enter the integral boundary value.
03:05q equals 19.6 coulombs.
03:10Here's the answer to this question.
03:15Happy learning, everyone!
03:17thePlus if you want.
03:18The
03:18You
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