Current wave form of an inductor

Question

If this voltage is applied to an ideal inductor. How will be the current waveform look like?

Kindly any one show me the graph for inductor current and if possible explain it. I shall be very grateful! (Voltage is in blue)

Answer 1

Kindly any one show me the graph for inductor current and if possible explain it. I shall be very grateful!

It's quite easy to do if you use a simulator (like Micro-cap): -

Voltage in blue and current through a 2 henry inductor in red. Timebase in seconds.

The current-voltage relationship for an inductor is: -

$$V = L\dfrac{di}{dt}$$

The above can be solved for current by integrating both sides.

$$i = \dfrac{1}{L}\int{v\: dt}$$

And, for a linearly rising voltage (\$v = V_{PK}\cdot t\$),

$$i = \dfrac{V_{PK}}{L}\int{t\: dt} = \dfrac{V_{PK}}{2L}t^2$$

Circuit: -

Slope of the current graph

This is just to show that visualizing the slope helps to understand the formula. I've got a green circle on the current graph and I've visually calculated the slope to be 5 amps per second. This corresponds with an applied voltage at that moment (blue circle) of 10 volts and, given that the inductance is 2 henry, the slope mathematically agrees because: -

$$\dfrac{V}{L} = \dfrac{di}{dt} = 5\text{ amps per second}$$