Question

The voltage and current are measured through a particular device and are found to be: v(t) = I 0 cos( 300t + 20° )V i(t) = 0.2 cos(300t + 45° )A If A<θ describes the complex power, what are A and θ? Enter A first, without units

Answer 1

Step-by-step explanation:

To find the complex power, we can use the formula:

S = V * I * conj(I) = V * I * I * / |I|^2

Plugging in the given values for V and I, we get:

S = (I0 * cos(300t + 20°)) * (0.2 * cos(300t + 45°)) * (0.2 * cos(-300t - 45°)) / |0.2 * cos(300t + 45°)|^2

This simplifies to:

S = (I0 * 0.2 * cos(300t + 20°) * cos(300t + 45°) * cos(-300t - 45°)) / (0.2^2 * cos^2(300t + 45°))

S = I0 * cos(300t + 20°) * cos(300t + 45°) * cos(-300t - 45°)

S = I0 * cos(300t + 20°) * cos(300t + 45°) * cos(300t + 45°)

S = I0 * cos(300t + 20°) * (cos^2(300t + 45°) + sin^2(300t + 45°))

S = I0 * cos(300t + 20°)

The magnitude of the complex power, A, is therefore equal to |I0 * cos(300t + 20°)|, and the angle, θ, is equal to 20°.

So, A = |I0 * cos(300t + 20°)| and θ = 20°.