To understand the collector current in the common emitter configuration of a Bipolar Junction Transistor (BJT), we must explore the relevant concepts and equations.

The common emitter configuration is widely used because it provides good voltage gain and is suitable for amplification purposes. In this configuration, the input is applied between the base and the emitter while the output is taken across the collector and the emitter.

The fundamental relationship between collector current (\(I_C\)), base current (\(I_B\)), and emitter current (\(I_E\)) in a BJT is governed by the following equations:

• The current gain in common emitter configuration is defined as \(\beta = \frac{I_C}{I_B}\).
• The emitter current \(I_E\) is the sum of the collector current and base current: \(I_E = I_C + I_B\).

Now let's establish the collector current \(I_C\) in terms of \(\beta\) and other parameters. Here's how it can be derived:

1. Start with the relation: \(I_C = \beta I_B + I_CBO\), where \(I_CBO\) is the reverse saturation current between collector and base when the emitter is open.
2. However, in practical scenarios and especially in the common emitter configuration, we are interested in the current relation considering the leakage current when the transistor is in active mode. This leakage current is termed \(I_{CEO}\), representing the leakage path.
3. Therefore, the correct expression for the collector current in common emitter configuration is: \(I_C = \beta I_B + I_{CEO}\).

Let's evaluate the provided options:

• \(\alpha I_E+I_{CBO}\): Uses \(\alpha\), which is related to common base configuration and does not emphasize \(I_B\) directly.
• \(\alpha I_E+I_{CEO}\): Similarly uses \(\alpha\) but does not suit common emitter contexts.
• \(\beta I_B+I_{CBO}\): Omits the important factor of leakage current in locked states without emphasizing \(I_{CEO}\).
• \(\beta I_B+I_{CEO}\): Correctly accounts for the common emitter scenario, including the common base leakage component \(I_{CEO}\).

Thus, the correct answer is \( \beta I_B + I_{CEO} \).