https://file.aiquickdraw.com/mathbot/file/1730294848624mw13lqzg.jpg

Let's solve for \( V_O \) and \( V_{CE} \) in this transistor circuit.

### Given Data:
1. \( V_{BE} = 0.7 \, \text{V} \)
2. \( \beta = 100 \)
3. \( R_B = 10 \, \text{k}\Omega \)
4. \( R_C = 500 \, \Omega \)
5. \( R_E = 200 \, \Omega \)
6. Supply voltages:
   - \( V_{CC} = 12 \, \text{V} \) (for the collector side)
   - \( V_{BB} = 5 \, \text{V} \) (for the base side)

### Step-by-Step Solution:

#### 1. **Calculate Base Current \( I_B \):**
Using Kirchhoff's Voltage Law (KVL) for the base circuit:
\[
V_{BB} = I_B R_B + V_{BE} + I_E R_E
\]
Since \( I_E = (1 + \beta) I_B \), we substitute \( I_E \) and rearrange to find \( I_B \):
\[
5 = I_B (10 \times 10^3) + 0.7 + I_B (1 + 100)(200)
\]
\[
5 = I_B (10,000 + 20,200)
\]
\[
I_B = \frac{5 - 0.7}{30,200} = \frac{4.3}{30,200} \approx 1.424 \, \mu A
\]

#### 2. **Calculate Collector Current \( I_C \):**
Using \( I_C = \beta I_B \):
\[
I_C = 100 \times 1.424 \, \mu A \approx 0.1424 \, \text{mA}
\]

#### 3. **Calculate \( V_O \):**
Using Ohm's law on the collector resistor \( R_C \):
\[
V_O = V_{CC} - I_C R_C
\]
\[
V_O = 12 - (0.1424 \times 500)
\]
\[
V_O = 12 - 0.0712 = 2.876 \, \text{V}
\]

#### 4. **Calculate \( V_{CE} \):**
The voltage \( V_{CE} \) is given by:
\[
V_{CE} = V_O - V_E
\]
Since \( V_E = I_E R_E \) and \( I_E \approx I_C \) (assuming \( \beta \) is large):
\[
V_E = 0.1424 \times 200 = 2.848 \, \text{V}
\]
\[
V_{CE} = 2.876 - 0.7 = 2.005 \, \text{V}
\]

### Answers:
1. \( V_O = 2.876 \, \text{V} \)
2. \( V_{CE} = 2.005 \, \text{V} \)

Would you like further details, or do you have questions?

### Related Questions:
1. How would changing \( \beta \) affect \( V_O \) and \( V_{CE} \)?
2. What happens to \( V_O \) if \( R_E \) is increased?
3. How would the circuit behave if \( V_{BE} \) was different?
4. How can we determine if the transistor is in saturation?
5. What is the role of \( R_C \) in setting the output voltage?

### Tip:
To verify if a transistor is in the active region, check if \( V_{CE} > V_{BE} \).

Calculate Vo and VCE in the transistor circuit assuming that the transistor is in the forward active mode with VBE = 0.7V and β = 100.

Step-by-step solution for calculating Vo and VCE in a transistor circuit, applying Kirchhoff's Voltage Law (KVL) and Ohm's Law. The circuit involves parameters VBE = 0.7V, β = 100, and uses resistors of 10kΩ, 500Ω, and 200Ω. Learn how to analyze the base, collector, and emitter currents to solve for the output voltage and VCE.

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