Question

A transistor is connected in CE configuration. The collector supply is 10 V and the voltage drop across a resistor of 1000 $ \Omega $ in the collector circuit is 0.5 V. If the current gain factor is 0.96, then the base current is

• A. 256 \( \mu A \)
• B. 20.8 \( \mu A \)
• C. 22.5 \( \mu A \)
• D. 15 \( \mu A \)

Hint:

The base current \( I_B \) can be found using the formula \( I_B = \frac{I_C}{\beta} \), where \( I_C \) is the collector current and \( \beta \) is the current gain factor.

Answer 1

The Correct Option is B

To solve the problem, we need to calculate the base current in the given transistor circuit using the provided parameters.

1. Given Information:
- Current gain factor, $\alpha = 0.96$
- Resistance of the collector resistor, $R = 1000 \, \Omega$
- Voltage drop across the collector resistor, $V_R = 0.5 \, \text{V}$

2. Calculate $\beta$:
The relationship between $\alpha$ and $\beta$ is given by:

$ \beta = \frac{\alpha}{1 - \alpha} $
Substitute $\alpha = 0.96$:

$ \beta = \frac{0.96}{1 - 0.96} = \frac{0.96}{0.04} = 24 $

3. Calculate Collector Current ($i_c$):
The collector current can be calculated using Ohm's Law:

$ i_c = \frac{V_R}{R} $
Substitute $V_R = 0.5 \, \text{V}$ and $R = 1000 \, \Omega$:

$ i_c = \frac{0.5}{1000} = 0.5 \times 10^{-3} \, \text{A} $

4. Calculate Base Current ($i_b$):
The relationship between collector current and base current is:

$ i_c = \beta \cdot i_b $
Rearrange to solve for $i_b$:

$ i_b = \frac{i_c}{\beta} $
Substitute $i_c = 0.5 \times 10^{-3} \, \text{A}$ and $\beta = 24$:

$ i_b = \frac{0.5 \times 10^{-3}}{24} = 0.020833 \times 10^{-3} \, \text{A} $
Convert to microamperes:

$ i_b = 20.833 \, \mu \text{A} $
Round to one decimal place:

$ i_b \approx 20.8 \, \mu \text{A} $

Final Answer:
The base current is $20.8 \, \mu \text{A}$.

Answer 2

To solve this problem, we need to determine the base current of the transistor given the collector voltage drop, resistance, and current gain factor.

1. Calculate the Collector Current ($I_C$):
The voltage drop across the collector resistor is given as 0.5 V, and the resistance is 1000 Ω. We can use Ohm's law to find the collector current:

$ I_C = \frac{V}{R} = \frac{0.5 \, \text{V}}{1000 \, \Omega} = 0.0005 \, \text{A} = 0.5 \, \text{mA} $

2. Understand the Current Gain Factor ($\alpha$):
The current gain factor in a common-emitter configuration is given as $\alpha = 0.96$. This represents the ratio of collector current to emitter current ($I_C/I_E$). 

The relation between $\beta$ and $\alpha$ is: $ \alpha = \frac{\beta}{\beta + 1} $, from this, we can derive $\beta = \frac{\alpha}{1-\alpha} $.

3. Calculate $\beta$ from $\alpha$:

$ \beta = \frac{0.96}{1-0.96} = \frac{0.96}{0.04} = 24 $

4. Determine the Base Current ($I_B$):
We know that $I_C = \beta \times I_B$. We can rearrange this to solve for $I_B$:

$ I_B = \frac{I_C}{\beta} = \frac{0.5 \, \text{mA}}{24} = \frac{0.0005 \, \text{A}}{24} = 0.000020833 \, \text{A} \approx 20.833 \, \mu\text{A} $

Final Answer:
The base current is approximately $ {20.8 \, \mu\text{A}} $.