Question

The ideal germanium diode at room temperature has a static resistance of 4.5ohm at a point, where the current flowing is 43.8mA. Find the dynamic resistance for a forward bias of 0.1 volt..

Answer 1

Hint: Dynamic resistance is also known as AC Forward resistance. You can use the formula for the dynamic resistance for a forward bias which can be defined as a ratio of change in voltage across the diode to the change in current through it.

Step by Step Solution:
 Ideal diode is a type of electrical component which functions like an ideal conductor when the voltage is used in the fore-way and an ideal insulator when the voltage is used in the reverse. Dynamic resistance for a forward bias can be calculated using the formula,
$ {r_f} = \dfrac{{\Delta V}} {{\Delta I}} $
Where ${r_f} $ is the dynamic resistance, $\Delta V$ is the change in voltage across the diode and $\Delta I$ is the change in current across the diode.
Firstly, we have to calculate the voltage across the diode when the resistance is static.
The formula for static resistance is
${R_f} = \dfrac{V}{I}$
Where ${R_f} $ is the static resistance, $V$ is the voltage across the diode and $I$ is the current flowing through the diode.
Given,
Static Resistance, ${R_f} = 4.5\Omega $
Current flowing through the diode, $I = 43.8mA$ OR $I = 0.0438A$
Therefore,
$V = 4.5 \times 0.0438$
$V = 0.1971volts$
Now, calculating the change in voltage across the diode,
$\Delta V = 0.1971 - 0.1$
$\Delta V = 0.0971volts$
The current through the germanium diode remains constant throughout therefore, we can right,
$\Delta I = 0.0438A$
Now, calculating the dynamic resistance across the germanium diode,
 ${r_f} = \dfrac{{\Delta V}} {{\Delta I}} $
${r_f} = \dfrac{{0.0971}}{{0.0438}}$
${r_f} = 2.25\Omega $
The dynamic resistance for a forward bias of $0.1volt$ is $2.25\Omega $

Note: The current passing through a diode can only go one way, which is called the forward direction. The reverse path is actually blocked to flow. It's like an automated one-way valve. If there is a negative voltage in the diode, then no current can flow and the ideal diode is an open circuit