Calculate the rms voltage of a rectangular wave - what is

Question

Question 1:

R = 100 Ω, L = 0.0049 H, and C = 5.2(10)^-6 F in the circuit

The input x(t) = v_i(t) in the circuit is given by x(t) = 10 cos(2Π 500 t) + 10 cos (2Π 1000 t)

The output y(t) = v_o(t) in the circuit is given by y(t) = K₁ cos (2Π 500 t + θ₁) + K₂ cos (2Π 1000 t + θ₂)

K₁, K₂, θ₁, and θ₂ are real-valued constants.

1. Find the numberical values for K₁, K₂, θ₁, and θ₂

2. Plot both the input x(t) and the output y(t) over the time range 0 ≤ t ≤ 2 ms

Question 2:

1. Calculate the rms voltage of a rectangular wave where V_L = -0.5 volt, V_H= 0.5 volt and t_L = t_H = 0.5 ms.

2. Calculate the rms voltage of a rectangular wave where V_L = 0 volt, V_H = 1 volt and t_L = t_H = 0.5 ms.

3. What is the duty cycle of the wave of question 2?

4. Calculate the rms voltage of a rectangular wave where V_L = 0 volt, V_H = 1 volt, and the duty cycle is 90%.

5. The rms voltage for a sine wave with zero offset is given by Vrms = 1/√2V_peak. Calculate the rms voltage for a sine wave with a peak-to-peak voltage of 1 V.

6. All of the above waves have peak-to-peak voltages of 1V. Which would deliver the most power to a resistor?

Question 3:

a) Find the current going through the 8Ω resistor

b) Find the current I.