Analyzing Voltage Waveforms in a Circuit

[thomas49th]

Homework Statement

In the circuit of Fig. 16(a), the voltage v has the periodic waveform shown in Fig. 16(b) with a period of 4 us and an amplitude of 20 V.

Homework Equations

i = Cdv/dt

v = Ldi/dt

The Attempt at a Solution

Assuming that x is constant (at its average value), draw a dimensioned sketch of the waveform
of iL(t) and determine its maximum and minimum values.

x = 5 (as duty cycle is 1/4 => 20/4)
Therefore at beginning of cycle v = 20 => inductor has drop of 15v across it

using v = Ldi/dt
di/dt = 15/2e-3
= 7500 Amp per sec
i = 7.5mA

So in one microsecond the current in the inductor goes from 0 to 7.5mA agreed? I've presumed the charge is linear, is this correct? Why?

Now after 1us the v is 0 volts for 3us. This means the inductor's magnetic field will collapse into the capacitor or resistor or both?

Thanks
Thomas

 

[Antiphon]

Nope. The current isn't starting up at zero.

You need to find the average current too (you have a resistor with an average voltage already so this is easy.)

The inductor current won't collapse. It will be a triangle wave up and down with the applied voltage riding on top of a steady DC current.

 

[thomas49th]

Okay the current to begin with is 20/R = 5/1000 = 5mA. Average current at iR = 5/1000 = 5mA through the resistor. Correct? Why is the shape straight lines (not exponentially stuff)

 

[thomas49th]

?

 

[DeeNos]

Your calculations for the current in the inductor are correct. However, it is important to note that the charge is not necessarily linear. The rate of change of current (di/dt) may vary depending on the circuit parameters and the shape of the waveform.

After 1us, the voltage is 0 volts for 3us, which means that there is no current flowing through the inductor. This also means that the magnetic field in the inductor will collapse, causing a change in the current in the circuit. This change in current will depend on the circuit parameters, such as the inductance and resistance.

The inductor's magnetic field will primarily collapse into the capacitor, as it is a component that can store energy in the form of an electric field. However, there may also be a small amount of energy dissipated in the resistor due to its resistance.

Overall, the waveform of iL(t) will have a similar shape to v(t), but with a different amplitude and phase shift. The maximum value of iL(t) will occur when the voltage across the inductor is at its maximum (20V) and the minimum value will occur when the voltage across the inductor is at its minimum (0V). The exact values will depend on the specific parameters of the circuit.