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Let's solve the problem step by step, where we need to find the resistances \( R_C \) and \( R_B \) for the given circuit.

### Given Data:
- \( V_{CC} = 10 \, \text{V} \)
- \( V_{BB} = 5 \, \text{V} \)
- \( I_C = 10 \, \text{mA} = 0.01 \, \text{A} \)
- \( V_{CE} = 5 \, \text{V} \)
- \( V_{BE} = 0.7 \, \text{V} \)
- \( \beta = 100 \) (current gain)
- Negligible reverse saturation current

### Step 1: Finding \( R_C \)

We can use Kirchhoff's Voltage Law (KVL) in the output loop:
\[
V_{CC} = I_C R_C + V_{CE}
\]
Rearranging to solve for \( R_C \):
\[
R_C = \frac{V_{CC} - V_{CE}}{I_C}
\]
Substitute the known values:
\[
R_C = \frac{10 \, \text{V} - 5 \, \text{V}}{0.01 \, \text{A}} = \frac{5 \, \text{V}}{0.01 \, \text{A}} = 500 \, \Omega
\]

So, \( R_C = 500 \, \Omega \).

### Step 2: Finding \( R_B \)

First, calculate the base current \( I_B \) using the relation between collector current \( I_C \) and \( I_B \):
\[
I_B = \frac{I_C}{\beta}
\]
Substitute the known values:
\[
I_B = \frac{0.01 \, \text{A}}{100} = 0.0001 \, \text{A} = 100 \, \mu\text{A}
\]

Next, apply KVL in the input loop:
\[
V_{BB} = I_B R_B + V_{BE}
\]
Rearranging to solve for \( R_B \):
\[
R_B = \frac{V_{BB} - V_{BE}}{I_B}
\]
Substitute the known values:
\[
R_B = \frac{5 \, \text{V} - 0.7 \, \text{V}}{0.0001 \, \text{A}} = \frac{4.3 \, \text{V}}{0.0001 \, \text{A}} = 43 \, \text{k}\Omega
\]

So, \( R_B = 43 \, \text{k}\Omega \).

### Final Answer:
- \( R_C = 500 \, \Omega \)
- \( R_B = 43 \, \text{k}\Omega \)

Would you like further details on the calculations or clarification on any steps?

Here are some related questions to further explore this topic:
1. How would changing the value of \( V_{CC} \) affect \( R_C \)?
2. What happens if \( \beta \) (current gain) is doubled?
3. How does the choice of \( R_B \) influence the stability of the circuit?
4. Can we calculate the emitter current \( I_E \) from the given values?
5. How would the circuit behavior change if \( V_{BE} \) is 0.6V instead of 0.7V?

**Tip**: In BJT circuits, small changes in \( \beta \) can significantly affect base current, so stability techniques (like feedback) are often used to minimize this impact.

Find Rc and Rb, in the circuit if Vcc = 10V and VBB = 5V, so that Ic = 10mA and VCE = 5V. A silicon transistor with beta = 100, VBE = 0.7V, and negligible reverse saturation current is under consideration.

Learn how to calculate Rc and Rb for a silicon transistor circuit where Vcc = 10V, VBB = 5V, Ic = 10mA, VCE = 5V, and beta = 100. This problem uses Kirchhoff's Voltage Law and basic transistor equations. Suitable for undergraduate electrical engineering students.

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