Question

For a transistor, in a common base configuration the alternating current gain \(\alpha\) is given by: (A) \(\left[\Delta \mathrm{I}_{\mathrm{C}} / \Delta \mathrm{I}_{\mathrm{B}}\right]_{(\mathrm{V}) \mathrm{C}=\mathrm{const}}\) (B) \(\left[\Delta \mathrm{I}_{\mathrm{B}} / \Delta \mathrm{I}_{\mathrm{C}}\right]_{(\mathrm{V}) \mathrm{C}=\mathrm{const}}\) (C) \(\left[\Delta \mathrm{I}_{\mathrm{C}} / \Delta \mathrm{I}_{\mathrm{E}}\right]_{(\mathrm{V}) \mathrm{C}=\text { const }}\) (D) \(\left[\Delta \mathrm{I}_{\mathrm{E}} / \Delta \mathrm{I}_{\mathrm{C}}\right]_{(\mathrm{V}) \mathrm{C}=\text { const }}\)

Short answer

In a common base configuration of a transistor, the alternating current gain (α) is given by: α = \( \frac{\Delta I_{C}}{\Delta I_{E}} \)_{(V_C)=const}. So, the correct option is (C).

Step-by-step solution

Understand Terminologies

Common-base configuration is an arrangement in which the input voltage is applied to the emitter and the output voltage is taken from the collector. In this configuration, the base terminal is used as a common ground for both input and output. We have given: - 𝑰𝑪: collector current - 𝑰𝑩: base current - 𝑰𝑬: emitter current - Δ: delta notation, represents change in the variable - 𝑣𝑪 = const: constant voltage across collector to emitter Step 2: Know the formula for Alternating Current Gain (α)

Know the formula for Alternating Current Gain (α)

In a common base configuration, the alternating current gain (α) is the change in collector current (Δ𝑰𝑪) divided by the change in emitter current (Δ𝑰𝑬), with a constant voltage across the collector and emitter. The formula can be given as: α = \( \frac{\Delta I_{C}}{\Delta I_{E}} \)_{(V_C)=const} Step 3: Identify the correct option

Identify the correct option

Now that we know the correct formula for alternating current gain (α) in a common base configuration, let's compare it with the given options: (A) \( \frac{\Delta I_{C}}{\Delta I_{B}} \)_{(V_C)=const} (B) \( \frac{\Delta I_{B}}{\Delta I_{C}} \)_{(V_C)=const} (C) \( \frac{\Delta I_{C}}{\Delta I_{E}} \)_{(V_C)=const} (D) \( \frac{\Delta I_{E}}{\Delta I_{C}} \)_{(V_C)=const} Comparing the correct formula (α = \( \frac{\Delta I_{C}}{\Delta I_{E}} \)_{(V_C)=const}) with the given options, we can see that the correct choice is (C).

Key concepts

Transistors

Transistors are essential components in modern electronics. They act as amplifiers and switches, controlling the flow of electrical current in circuits. Transistors have three main parts: the emitter, base, and collector.

• The Emitter releases carriers (electrons or holes), which flow through the transistor.
• The Base is the middle section that controls the number of carriers entering the collector. It is very thin compared to the emitter and collector.
• The Collector gathers the carriers released by the emitter, allowing a larger current to pass through.

Transistors are widely used in electronics due to their ability to amplify signals and switch currents with precision. They form the backbone of all digital circuits, including CPUs, memory units, and signal processors.

Alternating Current Gain

In a common base configuration of a transistor, alternating current gain (represented by \( \alpha \)) is a crucial parameter. This configuration involves connecting the base to both the input and output, while the emitter serves as the input and the collector as the output. The alternating current gain \( \alpha \) is defined as the ratio of the change in collector current to the change in emitter current. Mathematically, this is represented by:\[\alpha = \frac{\Delta I_{C}}{\Delta I_{E}}\]where \( \Delta I_{C} \) denotes the change in collector current and \( \Delta I_{E} \) is the change in emitter current, given a constant voltage across the collector and emitter (\( V_C \) = const). This gain indicates how effectively the transistor can amplify current, making it a vital factor in designing amplification circuits.

Collector Current

Collector current (\( I_C \)) is one of the three currents in a transistor, and it plays a significant role in defining the operation of the device. In a common base configuration, the collector current is the output current drawn through the collector terminal. This current is largely influenced by:

• The flow of carriers (electrons or holes) from the emitter.
• The voltage applied across the collector and the base.

The collector current is signified by its relation to the emitter current in the equation for alternating current gain \( \alpha \). As the collector current changes, it directly affects the gain and the transistor's ability to amplify the input signal. Hence, understanding the behavior of \( I_C \) is crucial for designing efficient transistor circuits.

Emitter Current

Emitter current (\( I_E \)) is the current that flows into the emitter of a transistor. It is of great importance because it determines the number of charge carriers entering the base. In a common base configuration, the emitter current is the input current given to the transistor. It is composed of the collector current \( I_C \) and the base current \( I_B \) combined:\[I_{E} = I_{C} + I_{B}\]The emitter current is key to understanding how transistors amplify signals. Since the emitter releases carriers into the base and the collector collects them, any change in \( I_E \) affects \( I_C \), making it essential for calculating the current gain \( \alpha \). Ensuring proper management and control of the emitter current is vital for a transistor to function as intended in electronic circuits.