Question

The voltage and current for a device (using the passive sign convention) are periodic functions with T = 20 ms described by

v(t) = {10V 0 < t < 12 ms
0 12 ms < t < 20 ms

i(t) = {7A 0 < t < 6 ms
-5A 6 ms < t < 10 ms
4A 10 ms < t < 20 ms

Determine the following:

The instantaneous power

Answer 1

The instantaneous power in an AC circuit is the product of the voltage and current at any given time.

Step-by-step explanation:

The instantaneous power in an AC circuit is given by the product of the current and voltage at any given time. In this case, the voltage and current functions are given as:

v(t) = 10V for 0 < t < 12ms, and 0 for 12ms < t < 20ms

i(t) = 7A for 0 < t < 6ms, -5A for 6ms < t < 10ms, and 4A for 10ms < t < 20ms

To determine the instantaneous power at a specific time, we multiply the voltage and current at that time. For example, at t = 2ms, the voltage is 10V and the current is 7A, so the instantaneous power would be 10V * 7A = 70W.

Similarly, you can calculate the instantaneous power at other times using the given voltage and current functions.

Answer 2

The instantaneous power is calculated by multiplying the instantaneous values of voltage and current, resulting in power outputs of 70W, -50W, 40W, and 0W in different time intervals of the given period.

Step-by-step explanation:

The student asked to determine the instantaneous power for a device where the voltage and current are periodic functions with a period T = 20 ms. The voltage function is expressed as v(t) = 10V for 0 < t < 12 ms and 0V for 12 ms < t < 20 ms. The current function is i(t) = 7A for 0 < t < 6 ms, -5A for 6 ms < t < 10 ms, and 4A for 10 ms < t < 20 ms.

To find the instantaneous power p(t), you have to multiply the instantaneous values of voltage and current at any given time. Therefore, we have the following scenarios for power calculation:

• P(t) = 10V * 7A = 70W for 0 < t < 6 ms
• P(t) = 10V * (-5A) = -50W for 6 ms < t < 10 ms
• P(t) = 10V * 4A = 40W for 10 ms < t < 12 ms
• P(t) = 0V * 4A = 0W for 12 ms < t < 20 ms

This shows that the device dissipates or generates power at different rates during different segments of the cycle, depending on the product of the voltage and current at any given instant.