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]

?