Question

Сила тока в проводнике сопротивлением R=10 Ом равномерно снижается от i0=3A до i=0 за 30 секунд. Определить количество теплоты Q выделившейся за это время в проводнике.

Answer 1

Ток меняется по закону

I = 3- t/10

Мгновенная теплота

dQ = I^2*R*dt = (90-6t+t^2/10)* dt

Полная теплота

Q= интеграл от dQ от 0 до 30

Q = 90t - 3t^2+ t^3/30 = 900 Дж

Answer 2

Calculation of Heat Generated in a Conductor

To determine the amount of heat generated in a conductor as the current decreases from i0 = 3A to i = 0 over a period of 30 seconds, we can use the formula:

Q = I^2 * R * t

Where: - Q is the amount of heat generated in Joules (J) - I is the current in Amperes (A) - R is the resistance of the conductor in Ohms (Ω) - t is the time in seconds (s)

In this case, the resistance of the conductor is given as R = 10 Ω.

Substituting the given values into the formula, we have:

Q = (i0^2 - i^2) * R * t

Q = (3^2 - 0^2) * 10 * 30

Simplifying the equation:

Q = 9 * 10 * 30

Q = 2700 J

Therefore, the amount of heat generated in the conductor over the given time period is 2700 Joules (J).