Question

A n-p-n transistor is used in common emitter made in an amplifier it. A change of \(40 \mu \mathrm{A}\) in the base current changes the output current by \(2 \mathrm{~mA}\) and \(0.04 \mathrm{~V}\) in input voltage. The current amplification factor is (A) 20 (B) 30 (C) 50 (D) 400

Short answer

The current amplification factor (β) of the given n-p-n transistor in common emitter mode is 50.

Step-by-step solution

Determine the given values

In this problem, we have: - Change in base current (ΔIb): 40 μA - Change in output current (ΔIc): 2 mA - Change in input voltage (ΔV): 0.04 V We need to determine the current amplification factor (β).

Convert the given values to the same unit

To be consistent with our calculations, we need to convert all values to the same unit. We will convert the given current values into Amperes (A). - ΔIb = 40 μA = 40 × 10^(-6) A - ΔIc = 2 mA = 2 × 10^(-3) A

Calculate the current amplification factor (β)

Now, we can calculate the current amplification factor (β) using the formula: β = ΔIc / ΔIb β = (2 × 10^(-3)) / (40 × 10^(-6))

Simplify the expression

By simplifying the expression, we get: β = 50

Choose the correct answer

Since the value of β is 50, we can choose the correct answer to be: (C) 50

Key concepts

Current Amplification Factor

The current amplification factor, denoted as \( \beta \), is a key parameter in transistor operation, particularly in amplifier circuits. It represents the ratio of change in output current (\( \Delta I_c \)) to the change in base current (\( \Delta I_b \)). By mathematically expressing this relationship, we have:\[\beta = \frac{\Delta I_c}{\Delta I_b}\]The current amplification factor gives insight into how effectively a transistor can increase the power of an input signal.

In practical terms:

• A higher \( \beta \) value indicates better amplification, meaning the transistor can deliver a higher output current in response to a small change in input current.
• Common \( \beta \) values for small signal transistors range from about 20 to 1000.

Understanding \( \beta \) is crucial for designing circuits that require precise control over amplification.

Common Emitter Configuration

The common emitter configuration is one of the most widely used setups for transistor amplifiers. It is called 'common emitter' because the emitter terminal serves as a common ground for both the base and collector circuits.

This configuration is popular because:

• It provides a moderate level of voltage amplification.
• It results in a significant amount of current amplification, making it suitable for driving larger loads.
• The phase of the output signal is inverted relative to the input signal.

An essential feature of this arrangement is the ease with which it can provide a large increase in both current and voltage, which is ideal for general amplification purposes across numerous electronic devices.

Base Current

The base current (\( I_b \)) is a small current that flows into the base terminal of a transistor. Although tiny compared to the collector current, base current plays a crucial role in a transistor's operation.

Key points about base current include:

• Its primary function is to control the larger collector current (\( I_c \)).
• In a typical npn transistor, a slight increase in base current can lead to a substantial increase in the collector current, thanks to the current amplification factor \( \beta \).
• Since it is much smaller, it's important to precisely control the base current to ensure the transistor operates within its designed range.

Understanding the relationship between \( I_b \) and \( I_c \) through \( \beta \) aids in configuring a transistor as an effective amplifier.

Output Current

Output current, commonly referred to as collector current (\( I_c \)), is the main current flow that a transistor modulates in amplification applications.

Here are important insights about output current:

• The collector current is primarily determined by the base current and the current amplification factor \( \beta \).
• The relationship \( I_c = \beta \times I_b \) indicates how changes in base current influence the collector current.
• Gaining control over \( I_c \) allows for precise handling of signal amplification, making it a crucial aspect of effective transistor design.

In amplifiers, the goal is to increase \( I_c \) to drive a load successfully, based on small variations in \( I_b \). Understanding this interplay is fundamental for the effective construction of amplifying circuits.