For a voltage divider bias circuit in CE configuration using NPN BJT transistor, Vcc = 10 V and the resistance at collector and emitter is Rc = 2 kΩ and RE = 500 Ω, respectively. (Assume DC current gain Beta of transistor as very high) Determine the approximate maximum value of collector current for the voltage divider bias circuit.

Explanation:

Voltage Divider Bias Circuit in CE Configuration

Problem Statement: For a voltage divider bias circuit in CE configuration using NPN BJT transistor, with given values of V_CC = 10 V, R_C = 2 kΩ, and R_E = 500 Ω, we are tasked to determine the approximate maximum value of the collector current (I_C) for the circuit, assuming a very high DC current gain (β).

Solution:

The maximum collector current (I_C) can be calculated by considering the saturation condition of the transistor, where the transistor acts as a closed switch. In this state, the voltage across the collector-emitter junction (V_CE) is approximately zero.

Step 1: Voltage Distribution in the Circuit

In the saturation condition, the voltage across the collector resistor (R_C) and emitter resistor (R_E) will be:

V_RC + V_RE = V_CC

Where:

• V_RC = Voltage drop across the collector resistor (R_C)
• V_RE = Voltage drop across the emitter resistor (R_E)

Step 2: Current Flow in the Circuit

The current flowing through R_C and R_E is the collector current (I_C), which is equal to the emitter current (I_E) in the saturation condition because the base current (I_B) is negligible for high β values.

Step 3: Maximum Collector Current Calculation

To calculate the maximum collector current (I_C), we use Ohm's Law:

I_C = I_E = V_CC ÷ (R_C + R_E)

Substituting the given values:

V_CC = 10 V, R_C = 2 kΩ = 2000 Ω, R_E = 500 Ω

I_C = 10 ÷ (2000 + 500)

I_C = 10 ÷ 2500

I_C = 0.004 A

I_C = 4 mA

Thus, the maximum collector current for the voltage divider bias circuit is approximately 4 mA.

Important Information

Let’s analyze other options:

Option 1: 5 mA

This value is incorrect because the calculation shows that the maximum collector current (I_C) is 4 mA, based on the circuit parameters. The resistance values and supply voltage do not support a collector current of 5 mA.

Option 3: 2.5 mA

This value is incorrect because it underestimates the current. Using the formula I_C = V_CC ÷ (R_C + R_E), the calculated value is 4 mA, not 2.5 mA.

Option 4: 20 mA

This value is incorrect because it overestimates the current. The resistance values and supply voltage do not support such a high collector current. The calculated maximum value is 4 mA.

Conclusion:

The correct option is Option 2, which gives the maximum collector current (I_C) as approximately 4 mA. This value aligns with the calculations based on the given circuit parameters, considering the saturation condition of the transistor and assuming a very high DC current gain (β).