https://file.aiquickdraw.com/mathbot/file/1726672128251a5m8vkxv.jpg

Let's analyze and solve the circuits shown in the image for current \( I \) using the approximate equivalent model for the diode. In this model, a silicon (Si) diode is assumed to have a forward voltage drop of approximately \( V_D = 0.7 \, \text{V} \) when conducting.

### Circuit (a):
1. **Voltage Source**: 12 V
2. **Resistor**: 10 Ω
3. **Silicon Diode**: Forward-biased with a 0.7 V drop when conducting.

To find the current \( I \) through the circuit:

- The voltage across the resistor is the difference between the source voltage and the diode's forward voltage.
  \[
  V_R = 12 \, \text{V} - 0.7 \, \text{V} = 11.3 \, \text{V}
  \]
- Using Ohm's law:
  \[
  I = \frac{V_R}{R} = \frac{11.3 \, \text{V}}{10 \, \Omega} = 1.13 \, \text{A}
  \]

### Circuit (b):
1. **Voltage Source**: 20 V
2. **Resistors**: 10 Ω and 20 Ω in series
3. **Two Silicon Diodes**: Each has a forward voltage drop of 0.7 V when conducting.

Since both diodes are forward biased, the total voltage drop across the two diodes is:
\[
V_{\text{total diode drop}} = 0.7 \, \text{V} + 0.7 \, \text{V} = 1.4 \, \text{V}
\]

- The remaining voltage across the series resistors is:
  \[
  V_R = 20 \, \text{V} - 1.4 \, \text{V} = 18.6 \, \text{V}
  \]
- The total resistance is \( R_{\text{total}} = 10 \, \Omega + 20 \, \Omega = 30 \, \Omega \).
- Using Ohm's law:
  \[
  I = \frac{V_R}{R_{\text{total}}} = \frac{18.6 \, \text{V}}{30 \, \Omega} = 0.62 \, \text{A}
  \]

### Circuit (c):
1. **Voltage Source**: 10 V
2. **Resistor**: 10 Ω
3. **Two Silicon Diodes**: In opposite directions.

In this case, one of the diodes is always reverse biased and blocks the current. So, no current flows through the circuit:
\[
I = 0 \, \text{A}
\]

### Summary:
- **(a)**: \( I = 1.13 \, \text{A} \)
- **(b)**: \( I = 0.62 \, \text{A} \)
- **(c)**: \( I = 0 \, \text{A} \)

Would you like further details on any of the steps or an explanation of the diode model used?

Here are some related questions:
1. How does the reverse bias affect current flow in a diode?
2. What is the difference between a silicon diode and a germanium diode in terms of voltage drop?
3. How would the current change in circuit (b) if the resistor values were different?
4. Why is there no current in circuit (c)?
5. What would happen in circuit (a) if the diode were replaced with a different type?

**Tip**: Always check whether the diode is forward or reverse biased to determine if it conducts current.

Determine the current I for each of the configurations of Fig. 2.155 using the approximate equivalent model for the diode.

This problem explores the determination of current in three different series diode configurations using the approximate equivalent model. We calculate current using Ohm's law and account for voltage drops across silicon diodes, highlighting concepts such as Kirchhoff's Voltage Law and diode characteristics. Suitable for undergraduate electrical engineering students.

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