The lonely diode

A diode is characterized by its I-V curve similar to the one above.

Consider a diode whose dynamic resistance is given by

\({ r }_{ dyn }(i)=\frac { { V }_{ d } }{ { (i+\beta ) }^{ 2 }\ }\beta \)
where \(i\) is the current and \(\beta \) and \({ V }_{ d }\) are characteristics of the diode.

This diode is connected from terminal to terminal with a conducting wire forming a loop. This planar loop has area \(A\) and is kept in a magnetic field \(B\), normal to its plane.

Find the average power dissipation (in nano-Joules) across the diode.

Given:

  • \({ V }_{ d }=0.9 V\)

  • \(\beta = 0.1 A\)

  • \(B = { B }_{ 0 }cos(100t)\) with \({ B }_{ 0 }= 1\mu T\)

  • \(A = 1 m ^2\)

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