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The diode in the next figure is considered ideal (i.e. works as a simple switch, being turned ON when $U_D \geq 0$ and OFF when $U_D < 0$). What is the voltage $U_S$ across $R_S$?

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I've assumed that the diode is OFF and replaced it with an open circuit. The conditions are: $U_D > 0, I_D = 0$. I think I should be applying KVL now to find the voltage, but I'm not sure how. Also, I've also taken into consideration using Thevenin's Theorem, but I get stuck at a point where I need to find $I_D$ in order to calculate $U_S$. However, I think the assumed states method is better in this case. Could you give me an idea on how to continue this?

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First note that if you're using the German (or East European) convention for the voltage polarity, the diode is ON when $U_D\ge 0$ and OFF when $U_D < 0$.

If you assume that the diode is OFF, that is, you assume $U_D < 0$, then you can ignore the branch with the diode and the circuit is a simple voltage divider with $U_S = E/2 = 6\,\mathrm{V}$. But since $U_D = U_S+E_0 = 9\,\mathrm{V} > 0$, this contradicts the assumption, and the diode is instead ON.

Now you can go on, knowing that the diode in the ON state behaves as a short circuit.

The picture below shows three different common ways of denoting the polarity of a voltage, with an indication of some example countries in which are frequently used (no pretense of being general or exhaustive, and variations are possible):

Different voltage polarity conventions

When reading circuits, it is important to properly interpret the conventions used to denote polarities.

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  • $\begingroup$ Thank you, could you please tell me how you got the 2 relations : $U_S = E/2$ and $U_D = U_S + E_0$? $\endgroup$ – Andrei0408 2 days ago
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    $\begingroup$ @Andrei0408 The first one is a simple application of the voltage divider's formula, taking into account that the two resistances are equal, $R=R_S$; the second one can be obtained by writing the Kirchhoff's voltage law at the loop containing the diode, $E_0$ and $U_S$. $\endgroup$ – Massimo Ortolano 2 days ago

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