Using the transistor values of:   β = 200, Ic = 4mA and Ib =  2.0 X 10-6 A

**, find the value of the Base resistor (Rb) required to switch the load "ON" when the input terminal voltage exceeds 2.5v.** 

To find the value of the base resistor (\( R_B \)) required to switch the transistor "ON" when the input terminal voltage exceeds 2.5 V, we need to use the following relationships between the base current (\( I_B \)), collector current (\( I_C \)), and base-emitter voltage (\( V_{BE} \)).

### Step 1: Transistor Current Relations

The collector current (\( I_C \)) and base current (\( I_B \)) are related by the transistor’s current gain (\( \beta \)):

\[
I_C = \beta I_B
\]

Given values:
- \( \beta = 200 \)
- \( I_C = 4 \, \text{mA} = 4 \times 10^{-3} \, \text{A} \)
- \( I_B = 2 \times 10^{-6} \, \text{A} \)

Using \( I_C = \beta I_B \), we can verify that:

\[
I_B = \frac{I_C}{\beta} = \frac{4 \times 10^{-3}}{200} = 2 \times 10^{-5} \, \text{A}
\]

So, the base current needed to achieve the desired collector current is \( I_B = 2 \times 10^{-5} \, \text{A} \).

### Step 2: Base-Emitter Voltage Assumption

For most standard transistors, the base-emitter voltage \( V_{BE} \) is around 0.7 V when the transistor is fully on (saturated). 

### Step 3: Applying Ohm’s Law

To find the base resistor \( R_B \), we can use Ohm's Law. The voltage across \( R_B \) is the difference between the input terminal voltage (\( V_{in} \)) and the base-emitter voltage \( V_{BE} \):

\[
R_B = \frac{V_{in} - V_{BE}}{I_B}
\]

Given:
- \( V_{in} = 2.5 \, \text{V} \)
- \( V_{BE} = 0.7 \, \text{V} \)
- \( I_B = 2 \times 10^{-5} \, \text{A} \)

Substitute these values into the formula:

\[
R_B = \frac{2.5 \, \text{V} - 0.7 \, \text{V}}{2 \times 10^{-5} \, \text{A}} = \frac{1.8 \, \text{V}}{2 \times 10^{-5} \, \text{A}} = 90,000 \, \Omega = 90 \, \text{k}\Omega
\]

### Final Answer:
The required base resistor \( R_B \) is **90 kΩ**.

---

Would you like more details on this calculation or further clarifications?

Here are five related questions to explore:
1. How would changing \( \beta \) to a lower value affect the required base resistor?
2. What would happen if \( V_{in} \) were reduced below 2.5V?
3. Can we assume \( V_{BE} = 0.7 \, \text{V} \) for all transistors, or does it vary?
4. What are the implications of using a higher base resistor than calculated?
5. How does saturation affect the transistor’s switching performance?

**Tip:** Ensure that the base current is sufficient to saturate the transistor to fully switch it on.

Using the transistor values of: β = 200, Ic = 4mA and Ib = 2.0 X 10-6 A, find the value of the Base resistor (Rb) required to switch the load 'ON' when the input terminal voltage exceeds 2.5v.

Learn how to calculate the base resistor (Rb) required to switch a transistor 'ON' with β = 200, Ic = 4mA, and Vin = 2.5V. This solution covers key concepts like Ohm's Law and transistor current relations. Suitable for Grades 10-12, this problem provides a step-by-step explanation of determining Rb using Ic, Ib, and Vbe.

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