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).