The current in the conductor changes according to the law I = 3 + 2t. During the time t1 = 3 to t2 = 6 s, a number of electrons

The current in the conductor changes according to the law I = 3 + 2t. During the time t1 = 3 to t2 = 6 s, a number of electrons will pass through the cross-section of the conductor, equal to …

Given:

I (t) = 3 + 2 * t – the equation of the dependence of the current strength on time;

t1 = 3 seconds – time interval;

e = 1.6 * 10 ^ -19 – electron charge;

t2 = 6 seconds – time span.

It is required to determine how many electrons n will pass through the conductor during the time from t1 to t2.

From the equation of the dependence of the current strength on time, we see that the current strength changes in a linear manner. Then, the total charge passed during this time will be equal to:

I1 = 3 + 2 * t1 = 3 + 2 * 3 = 3 + 6 = 9 Amperes;

I2 = 3 + 2 * t2 = 3 + 2 * 6 = 3 + 12 = 15 Amperes;

dt = t2 – t1 = 6 – 3 = 3 seconds;

Q = I1 * dt + dt * (I2 – I1) / 2 = 9 * 3 + 3 * (15 – 9) / 2 = 27 + 9 = 36 Coulomb.

Then the number of electrons will be equal to:

n = Q / q = 36 / (1.6 * 10 ^ -19) = 22.5 * 10 ^ 19 = 2.25 * 10 ^ 20.

Answer: The number of electrons is 2.25 * 10 ^ 20.