Question

The silicon diode shown in the figure is rated for a maximum current of $$100mA$$. Calculate the minimum value of the resistance of the resistor to avoid breakdown of diode. Assume the voltage drop across the diode to be $0.7V$.

A. $70\Omega $
B. $16\Omega $
C. $193\Omega $
D. $39\Omega $

Answer 1

Hint: The figure above represents the V-I characteristics of P-N junction when the junction is forward biased. Here, firstly we will Ohm’s law to calculate the voltage across the circuit, and then we will calculate the resistance required to avoid breakdown of the diode by using Ohm’s law. The breakdown of the p-n junction diode usually occurs when a high reverse voltage is applied to the diode.

Complete step by step answer:
In the circuit given in the question, the P junction of the diode is connected to the positive terminal of the voltage and the N junction is connected to the negative terminal, therefore the junction is forward biased.
Now, the voltage of the circuit can be calculated by using the following formula
$V = IR$
Now, it is clear from the above equation that the voltage is proportional to the current, therefore, the current increases with an increase in the voltage.
Now, the above equation can be written as
$R = \dfrac{V}{I}$
As the current is inversely proportional to the resistance then we can say that the current is maximum when the resistance is minimum.
Now, we are given in the question,
$\eqalign{
  & I = 100mA \cr
  & \Rightarrow \,I = 100 \times {10^{ - 3}}A \cr
  & \therefore \,I = 0.1\,A \cr} $
Now the voltage applied to the junction is $20\,V$ and the voltage drop across the diode is $0.7V$.
Therefore, the voltage across the circuit is given by
$\eqalign{
  & V = 20\,V - 0.7V \cr
  & \Rightarrow V = 19.3\,V \cr} $
Now, the resistance of the resistor is given by
$R = \dfrac{V}{I}$
$ \Rightarrow R = \dfrac{{19.3}}{{0.1}}$
$ \Rightarrow \,R = 193\Omega $
Therefore, the minimum resistance of the resistor to avoid breakdown of diode is $193\Omega $.

So, the correct answer is “Option C”.

Note:
In the forward-biased P-N junction, the voltage is applied to overcome the potential barrier. Once the external voltage increases the value of potential barrier voltage then the P-N junction diode will behave as an ordinary conductor. Also, the resistance in this case will be less and the depletion layer will be thin.