Question

The voltage-current characteristic of a diode during forward bias is given by $I=7.8\times 10^{-5}{e}^{6.5V_D}$, where $I$ is the current in $mA$ and $V_D$ is the diode voltage in $V$. Find the dynamic resistance of the diode in $\Omega$, when the current is $4mA$.

• A. 18.6
• B. 21.7
• C. 28.2
• D. 36.2

Answer 1

Answer: (D)

Differentiating $I_D$ w.r.t. $V_D$, we get
$\frac{d}{d{V}_D}\left(I_D\right)=\frac{d}{d{V}_D}\left(7.8\times 10^{-5}{e}^{6.9V_D}\right)$
$=7.8\times 10^{-5}\times 6.9\times e^{6.9V_D}$
$=I_D\times 6.9$
Dynamic resistance is $\frac{d}{d{I}_D}\left(V_D\right)$
$\Rightarrow \frac{d{V}_D}{d{I}_D}=\frac{1}{6.9\times I_D}$
When $I_D=4mA=4\times 10^{-3}A$
Then,
$\frac{d{V}_D}{d{I}_D}=\frac{1}{6.9\times 4\times 10^{-3}}$
$=36.23\Omega$
$\therefore$ Dynamic resistance $=36.23\Omega$