Question

What is the need of doping of intrinsic semiconductors? Ideal diodes are used in the given circuits. Find the value of current in both the circuits.

Hint:

An ideal diode is a short when forward biased and an open when reverse biased. A series diode string conducts only if all diodes are forward; then \(I=V/R=2/10=0.2\) A, otherwise 0.

Answer 1

Step 1: Why intrinsic semiconductors are doped.
In a pure semiconductor the number of electrons equals the number of holes and both are very small, giving poor conductivity that also changes sharply with temperature. By deliberately adding impurity atoms (doping) we raise one type of carrier enormously, obtain a stable and much higher conductivity, and create the n-type and p-type materials needed to build junctions.

Step 2: Ideal-diode model.
Forward bias \(\Rightarrow\) short circuit (0 V drop, 0 \(\Omega\)). Reverse bias \(\Rightarrow\) open circuit (no current). A series string of diodes conducts only if every diode in it is forward biased.

Step 3: Analyse the first loop.
The three diodes in the first loop all face the direction in which the 2 V source pushes current, so each is a short. The loop reduces to a 2 V source across a single 10 \(\Omega\) resistor: \[I_1=\frac{2\ \text{V}}{10\ \Omega}=0.2\ \text{A}.\]
Step 4: Analyse the second loop.
The reversed diode in the second loop is an open switch for the source's push, breaking the series path, so no steady current can flow: \[I_2=0.\]
Step 5: Result.
The first circuit carries 0.2 A; the second carries no current. \[\boxed{I_1=0.2\ \text{A},\ \ I_2=0\ \text{A}}\]