Question

In a transistor, a change of \(8.0 \mathrm{~mA}\) in the emitter current produces a change of \(7.8 \mathrm{~mA}\) in the collector current. What change in the base current is necessary to produce the same change in the collector current? (A) \(300 \mu \mathrm{A}\) (B) \(400 \mu \mathrm{A}\) (C) \(200 \mu \mathrm{A}\) (D) \(100 \mu \mathrm{A}\)

Short answer

The change in base current necessary to produce the same change in the collector current is (C) \(200 \mu \mathrm{A}\).

Step-by-step solution

Understand the relationship between emitter, base, and collector currents

In any transistor, the emitter current (I_E) is the sum of the collector current (I_C) and the base current (I_B), as shown by the following equation: \(I_E = I_B + I_C\)

Calculate the initial base current

We have to initially find the base current (I_B) before the change in emitter current. According to the problem, the change in the emitter current (\(ΔI_E\)) is 8.0 mA and the change in the collector current (\(ΔI_C\)) is 7.8 mA. We can use these values to find the change in base current (\(ΔI_B\)): \(ΔI_E = ΔI_B + ΔI_C\) \(ΔI_B = ΔI_E - ΔI_C\) Substituting the given values, \(ΔI_B = 8.0\; mA - 7.8\;mA\)

Calculate the change in base current

Now, compute the change in base current required (\(ΔI_B\)) to produce the same change in collector current: \(ΔI_B = 8.0\; mA - 7.8\;mA\) \(ΔI_B = 0.2\; mA\) Since the options are given in microamperes (μA), we can convert the change in base current from mA to μA: \(ΔI_B = 0.2\; mA * 1000\; (1\; mA = 1000\; μA)\) \(ΔI_B = 200\; μA\)

Identify the correct option

Now that we have calculated the change in base current necessary to produce the same change in the collector current, we can identify the correct option. The answer is: (C) \(200 \mu \mathrm{A}\)

Key concepts

Understanding Emitter Current

When discussing transistors, the **emitter current** is one of the primary parameters to understand. The emitter current ( I_E ) is the total current that flows out of the transistor's emitter terminal. It serves as the source of all currents within the transistor.

• It's important to note that the emitter current is the sum of the collector current ( I_C ) and the base current ( I_B ).
• Mathematically, this is expressed as I_E = I_C + I_B . This equation is fundamental, as it allows us to analyze and compute various changes in current within a transistor circuit.

For instance, if you observe a change in the emitter current, you can determine how it will influence the collector current and the base current.
The exercise refers to a change in the emitter current by 8.0 mA, indicating that the other currents will adjust according to this primary change.

Examining Collector Current

The **collector current** ( I_C ) is crucial, as it generally carries the main load current in a transistor. It's typically the largest component of the emitter current in a bipolar junction transistor (BJT).

• The collector current is controlled by both the base current and the applied voltages in the circuit.
• In the exercise, the collector current changes by 7.8 mA when there's a change in the emitter current of 8.0 mA.

We infer that the collector current is highly influenced by changes in the emitter current, which hints at the high current gain properties of typical transistors. By understanding how these currents interrelate, we can efficiently analyze the behavior of the transistor in different circuits, making reliable predictions about its operation.
Knowing how the collector current operates allows us to calculate other currents within the transistor, such as the base current.

Calculating Base Current

The **base current** ( I_B ) is a smaller current compared to both the emitter and collector currents. However, it plays a significant role in determining the operation of the transistor.

• The base current acts as a control current. It allows management of the much larger collector current, I_C
• Using the relationship: I_E = I_B + I_C , you can calculate the base current if the other two are known.

In the given exercise, we calculated the necessary change in the base current required to result in the observed change in the collector current, considering a specific change in the emitter current. This led to determining ΔI_B , which showed a value of 0.2 mA or 200 μA when adjusted to microamperes. This small change in the base current allows the collector current to adjust as desired, demonstrating the controlling role of I_B .

Exploring Current Change Calculations

When dealing with transistor currents, **current change calculations** are essential to predict how changes propagate through a circuit.

• The equation ΔI_E = ΔI_B + ΔI_C helps determine how a change in one current affects the others.
• In the exercise, a change in ΔI_E by 8.0 mA results in a ΔI_C of 7.8 mA, indicating a need for precision in computing the necessary ΔI_B.

We computed the required ΔI_B as:\[ΔI_B = ΔI_E - ΔI_C = 8.0 ext{ mA} - 7.8 ext{ mA} = 0.2 ext{ mA}\]To convert this into microamperes:\[ΔI_B = 0.2 ext{ mA} \times 1000 = 200 ext{ μA}\]This calculation indicates how a small modulation in the base current can control larger changes in the collector current, showcasing the transistor's sensitivity and the meticulous nature of analyzing electronic circuits.