Problem

Determine the static or dc resistance of the commercially available diode of Fig. at a rev...

Determine the static or dc resistance of the commercially available diode of Fig. at a reverse voltage of –10 V. How does it compare to the value determined at a reverse voltage of –30 V?

FIG. Silicon semiconductor diode characteristics.

Step-by-Step Solution

Solution 1

Refer to the diode characteristics of Figure \(1.15\) in the text book.

Dashed line plot in the characteristics is for \(V_{D}<0 \mathrm{~V}\).

Blue colour line in the characteristics is for \(V_{D}>0 \mathrm{~V}\).

The diode reverse voltage is, \(V_{D} \cong-10 \mathrm{~V}\).

Consider dashed line in the characteristics since the diode reverse voltage is \(V_{D}<0 \mathrm{~V}\)

From Figure \(1.15\), the diode current at \(V_{D} \cong-10 \mathrm{~V}\) is,

$$ I_{D}=-10 \mathrm{pA} $$

Calculate the static or the dc resistance \(R_{D C}\).

$$ R_{D C}=\frac{V_{D}}{I_{D}} $$

Substitute \(-10 \mathrm{pA}\) for \(I_{D}\) and \(-10 \mathrm{~V}\) for \(V_{D}\).

$$ \begin{aligned} R_{D C} &=\frac{-10 \mathrm{~V}}{-10 \mathrm{pA}} \\ &=10^{12} \Omega \\ &=1000 \mathrm{G} \Omega \end{aligned} $$

Hence, the static or the dc resistance \(R_{D C}\) is \(1000 \mathrm{G} \Omega\).

The diode reverse voltage is, \(V_{D} \cong-30 \mathrm{~V}\).

Consider dashed line in the characteristics since the diode reverse voltage is \(V_{D}<0 \mathrm{~V}\)

From Figure \(1.15\), the diode current at \(V_{D} \cong-30 \mathrm{~V}\) is,

$$ I_{D}=-10 \mathrm{pA} $$

Calculate the static or the dc resistance \(R_{D C}\).

$$ R_{D C}=\frac{V_{D}}{I_{D}} $$

Substitute \(-10 \mathrm{pA}\) for \(I_{D}\) and \(-30 \mathrm{~V}\) for \(V_{D}\).

$$ \begin{aligned} R_{D C} &=\frac{-30 \mathrm{~V}}{-10 \mathrm{pA}} \\ &=3 \times 10^{12} \Omega \\ &=3000 \mathrm{G} \Omega \end{aligned} $$

Hence, the static or the dc resistance \(R_{D C}\) is \(3000 \mathrm{G} \Omega\).

It is clear that the static resistance \(R_{D C}\) for \(V_{D} \cong-30 \mathrm{~V}\) is more than for \(V_{D} \cong-10 \mathrm{~V}\).

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