Calculate the heat energy produced in 2 minutes the following currents flowing through a circuit having a total resistance of 15 ohm:
a) direct current of 8,75 A
b)an alternating current described by the equation i= 8,75 sin(200 pie t × 57,3) A
a) To calculate the heat energy produced by a direct current, we can use the formula:
Heat energy (Joules) = Current^2 * Resistance * Time
Given:
Current (I) = 8.75 A
Resistance (R) = 15 ohm
Time (t) = 2 minutes = 120 seconds
Plugging in these values, we get:
Heat energy = (8.75 A)^2 * 15 ohm * 120 s
Heat energy = 765.625 * 15 * 120
Heat energy = 13,781,250 J
Therefore, the heat energy produced by the direct current in 2 minutes is 13,781,250 Joules.
b) To calculate the heat energy produced by an alternating current, we need to integrate the instantaneous power over time. The instantaneous power can be calculated as:
Instantaneous power = Current^2 * Resistance
Given:
Current (I) = 8.75 sin(200πt × 57.3) A
Resistance (R) = 15 ohm
To calculate the heat energy, we need to integrate the power over time from t = 0 to t = 120 seconds:
Heat energy = ∫(0 to 120) [ (I^2) * R ] dt
However, the integration of the given equation requires complex calculus, and hence we cannot provide the exact numerical value of the heat energy produced by the alternating current. To calculate it accurately, numerical methods or software tools like MATLAB or Mathematica can be employed.