Let `I_E,I_C and I_B` represent the emitter current,the collector current and the base current respectively in a transistor.then

Options

A. `i_C`is slightly smaller than `i_E`
B. `i_C`is slightly greater than `i_E`
C. `i_B`is much smaller than `i_E`
D. `i_B`is much greater than `i_E`.

Answer

To solve the question regarding the relationships between the emitter current (I_E), collector current (I_C), and base current (I_B) in a transistor, we can follow these steps:

### Step 1: Understand the Transistor Configuration
In a typical bipolar junction transistor (BJT), there are three regions: the emitter, base, and collector. The emitter is heavily doped to inject carriers (electrons in NPN or holes in PNP), the base is lightly doped and thin, and the collector is moderately doped.

**Hint:** Remember that the emitter region is designed to inject carriers into the base.

### Step 2: Analyze the Current Flow
- The emitter current (I_E) is the total current flowing out of the emitter.
- The base current (I_B) is the current that flows into the base region.
- The collector current (I_C) is the current that flows out of the collector.

The relationship between these currents can be expressed as:
\[ I_E = I_B + I_C \]

**Hint:** This equation is based on the principle of conservation of charge in the transistor.

### Step 3: Compare I_B and I_E
In a transistor, the base current (I_B) is typically much smaller than the emitter current (I_E) because most of the carriers injected from the emitter into the base recombine with holes in the base, and only a small fraction of them continue to the collector.

Thus, we can conclude:
\[ I_B \ll I_E \]

**Hint:** Think about how many carriers recombine in the base compared to how many are injected.

### Step 4: Compare I_C and I_E
The collector current (I_C) is slightly less than the emitter current (I_E) because some of the carriers that enter the base recombine there and do not reach the collector. Therefore, we can express this relationship as:
\[ I_C < I_E \]

However, I_C is not significantly less than I_E; it is only slightly smaller due to the recombination in the base.

**Hint:** Consider the losses in the base due to recombination when thinking about I_C.

### Step 5: Summarize the Findings
Based on the analysis:
1. **I_B is much smaller than I_E** (Correct)
2. **I_C is slightly smaller than I_E** (Correct)
3. **I_C is not greater than I_E** (Incorrect)
4. **I_B is not greater than I_E** (Incorrect)

### Conclusion
From the above analysis, the correct options are:
- I_B is much smaller than I_E (Option 3)
- I_C is slightly smaller than I_E (Option 1)

### Final Answer
The correct options are:
- Option 1: I_C is slightly smaller than I_E
- Option 3: I_B is much smaller than I_E