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 8,87 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 Q = I^2 * R * t, where Q is the heat energy in Joules, I is the current in Amperes, R is the resistance in Ohms, and t is the time in seconds.
Given:
I = 8.87 A
R = 15 Ohm
t = 2 minutes = 2 * 60 = 120 seconds
Using the formula:
Q = (8.87^2) * 15 * 120
= 7021.624 Joules
Therefore, the heat energy produced in 2 minutes by a direct current of 8.87 A through a circuit with a total resistance of 15 Ohm is 7021.624 Joules.
b) To calculate the heat energy produced by an alternating current, we can use the formula Q = (I^2 * R * t) / 2, where Q is the heat energy in Joules, I is the RMS current in Amperes, R is the resistance in Ohms, and t is the time in seconds.
Given:
I = 8.75 sin(200 pi t × 57.3) A (Assuming this is the RMS value of the alternating current)
R = 15 Ohm
t = 2 minutes = 2 * 60 = 120 seconds
Using the formula:
Q = ((8.75^2) * 15 * 120) / 2
= 7670.3125 Joules
Therefore, the heat energy produced in 2 minutes by an alternating current described by the equation i= 8.75 sin(200 pi t × 57.3) A through a circuit with a total resistance of 15 Ohm is 7670.3125 Joules.