MP Board · Class 12 · Physics · Semiconductor ElectronicsA silicon diode has a threshold voltage of 0.7 V. It is connected in series with a 200 $\Omega$ resistor and a 5 V DC battery. Calculate: (i) the circuit current, (ii) the potential drop across the resistor, and (iii) the dynamic resistance if the current changes from 10 mA to 15 mA when the voltage changes by 0.1 V.

Given Data:

• Threshold voltage of silicon diode ($V_0$) = $0.7\text{ V}$
• Resistance ($R$) = $200\text{ }\Omega$
• Battery Voltage ($V$) = $5\text{ V}$

(i) Calculation of Circuit Current ($I$):\nWhen the diode is forward-biased and conducting, the effective voltage driving the current through the circuit is the battery voltage minus the threshold voltage of the diode.

$$\text{Effective Voltage } (V_{\text{eff}}) = V - V_0$$ $$V_{\text{eff}} = 5\text{ V} - 0.7\text{ V} = 4.3\text{ V}$$ \nUsing Ohm's Law, the circuit current $I$ is given by:

$$I = \frac{V_{\text{eff}}}{R}$$ $$I = \frac{4.3\text{ V}}{200\text{ }\Omega} = 0.0215\text{ A} = 21.5\text{ mA}$$
Answer (i): The circuit current is $21.5\text{ mA}$.

(ii) Calculation of Potential Drop across the Resistor ($V_R$):\nThe potential drop across the resistor $R$ can be calculated using Ohm's Law:

$$V_R = I \times R$$ $$V_R = 0.0215\text{ A} \times 200\text{ }\Omega = 4.3\text{ V}$| Answer (ii): The potential drop across the resistor is $4.3\text{ V}$.

(iii) Calculation of Dynamic Resistance ($r_d$):\nDynamic resistance is defined as the ratio of a small change in voltage to the corresponding small change in current.

$$\Delta V = 0.1\text{ V}$$ $$\Delta I = 15\text{ mA} - 10\text{ mA} = 5\text{ mA} = 5 \times 10^{-3}\text{ A}$$
\nUsing the formula for dynamic resistance:

$$r_d = \frac{\Delta V}{\Delta I}$$ $$r_d = \frac{0.1\text{ V}}{5 \times 10^{-3}\text{ A}} = \frac{0.1}{0.005} = 20\text{ }\Omega$$ Answer (iii): The dynamic resistance is $20\text{ }\Omega$.