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(200πt × 57,3) A
a) To calculate the heat energy produced in a circuit, we can use the formula:
Heat energy = (current^2) * resistance * time
Given:
Current (I) = 8.75 A
Resistance (R) = 15 Ω
Time (t) = 2 minutes
Substituting the values into the formula:
Heat energy = (8.75^2) * 15 * 120 seconds [since 2 minutes = 120 seconds]
Calculating:
Heat energy = (76.5625) * 15 * 120
Heat energy = 137906.25 Joules
Therefore, the heat energy produced in 2 minutes with a direct current of 8.75 A flowing through a circuit with a total resistance of 15 ohms is 137906.25 Joules.
b) The given alternating current equation is i = 8.75 sin(200πt × 57.3) A.
To calculate the heat energy produced, we need to find the average value of the current with respect to time, as the heat energy produced is proportional to the square of the current.
The average value of a sinusoidal current waveform over one complete cycle is zero. However, when squared, the average value becomes non-zero.
For a sine waveform, the average value when squared is (maximum value / 2)^2 = (8.75 / 2)^2 = 1.515625 A^2.
Using this average current value, we can calculate the heat energy:
Heat energy = (average current^2) * resistance * time
Heat energy = (1.515625^2) * 15 * 120 seconds [since 2 minutes = 120 seconds]
Calculating:
Heat energy = (2.293701171875) * 15 * 120
Heat energy = 4138.662109375 Joules
Therefore, the heat energy produced in 2 minutes with an alternating current described by the equation i = 8.75 sin(200πt × 57.3) A flowing through a circuit with a total resistance of 15 ohms is approximately 4138.66 Joules.