https://file.aiquickdraw.com/mathbot/file/17292091556261u1t70me.jpg

To solve for the DC values and other requested parameters, let's break down the circuit first.

### Given Data from the circuit:

- \( V_{CC} = 15 \, V \)
- \( \beta_{DC} = 90 \)
- \( R_1 = 22 \, k\Omega \)
- \( R_2 = 4.7 \, k\Omega \)
- \( R_C = 2.2 \, k\Omega \)
- \( R_E = 1.0 \, k\Omega \)
- Capacitors \( C_1 \) and \( C_2 \) are for AC signals, so we will ignore them for the DC analysis.

### Step 1: Determine \( V_B \) (Base Voltage)

The base voltage \( V_B \) is determined using the voltage divider formed by \( R_1 \) and \( R_2 \). The formula is:

\[
V_B = V_{CC} \times \frac{R_2}{R_1 + R_2}
\]

Substituting the values:

\[
V_B = 15 \, V \times \frac{4.7 \, k\Omega}{22 \, k\Omega + 4.7 \, k\Omega} = 15 \, V \times \frac{4.7}{26.7} = 2.64 \, V
\]

### Step 2: Determine \( V_E \) (Emitter Voltage)

The emitter voltage \( V_E \) can be approximated as:

\[
V_E = V_B - V_{BE}
\]

Where \( V_{BE} \) is typically around \( 0.7 \, V \) for a silicon transistor. So,

\[
V_E = 2.64 \, V - 0.7 \, V = 1.94 \, V
\]

### Step 3: Determine \( I_E \) (Emitter Current)

Using Ohm’s Law, the emitter current \( I_E \) is given by:

\[
I_E = \frac{V_E}{R_E}
\]

Substituting the values:

\[
I_E = \frac{1.94 \, V}{1.0 \, k\Omega} = 1.94 \, mA
\]

### Step 4: Determine \( I_C \) (Collector Current)

The collector current \( I_C \) is related to the emitter current \( I_E \) through the relationship:

\[
I_C \approx I_E \quad (\text{since} \ I_C \approx I_E \ \text{for large } \beta)
\]

Thus, \( I_C = 1.94 \, mA \).

### Step 5: Determine \( V_C \) (Collector Voltage)

The collector voltage \( V_C \) can be found using:

\[
V_C = V_{CC} - I_C \times R_C
\]

Substituting the values:

\[
V_C = 15 \, V - (1.94 \, mA \times 2.2 \, k\Omega) = 15 \, V - 4.268 \, V = 10.732 \, V
\]

### Step 6: Determine \( R_{total} \) and \( I_{total} \)

1. **Total resistance \( R_{total} \)** seen from the power supply is the equivalent resistance of \( R_1 \), \( R_2 \), and the emitter circuit. For DC analysis, the equivalent resistance of the biasing resistors \( R_1 \) and \( R_2 \) is their parallel combination:

\[
R_{total} = \left( \frac{R_1 \times R_2}{R_1 + R_2} \right) + R_C + R_E
\]

\[
R_{total} = \left( \frac{22 \, k\Omega \times 4.7 \, k\Omega}{22 \, k\Omega + 4.7 \, k\Omega} \right) + 2.2 \, k\Omega + 1.0 \, k\Omega
\]

\[
R_{total} = 3.863 \, k\Omega + 2.2 \, k\Omega + 1.0 \, k\Omega = 7.063 \, k\Omega
\]

2. **Total current \( I_{total} \)** from the power supply is:

\[
I_{total} = \frac{V_{CC}}{R_{total}} = \frac{15 \, V}{7.063 \, k\Omega} = 2.12 \, mA
\]

---

Let me know if you need further details or clarifications on any step.

Here are some follow-up questions for you:

1. What role do \( C_1 \) and \( C_2 \) play in the circuit?
2. How would changing \( R_E \) affect \( V_E \) and \( I_C \)?
3. What happens if \( V_{BE} \) is different from 0.7 V? 
4. How can you estimate the gain of this amplifier?
5. What is the significance of \( \beta_{ac} \) versus \( \beta_{DC} \)?

**Tip:** The emitter resistor \( R_E \) provides stability by reducing the effect of changes in \( \beta \) on the operating point of the transistor.

Determine the following DC values for the amplifier: (a) VB (b) VE (c) IE (d) IC (e) VC. Also, what would be R total and I total?

Learn how to calculate the DC values of a transistor amplifier circuit, including VB, VE, IE, IC, and VC. This guide also explains how to determine the total resistance (R total) and current (I total) using key concepts such as Ohm's Law and voltage divider rule.

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