Question

What is the relation of the transistor current? (A) \(\mathrm{I}_{\mathrm{B}}=\mathrm{I}_{\mathrm{C}}+\mathrm{I}_{\mathrm{E}}\) (B) \(\mathrm{I}_{\mathrm{C}}=\mathrm{I}_{\mathrm{E}}+\mathrm{I}_{\mathrm{B}}\) (C) \(\mathrm{I}_{\mathrm{E}}=\mathrm{I}_{\mathrm{C}}+\mathrm{I}_{\mathrm{B}}\) (D) \(\mathrm{I}_{\mathrm{C}}=\mathrm{I}_{\mathrm{E}}+\mathrm{I}_{\mathrm{B}}\)

Short answer

The short answer is: (C) \(\mathrm{I}_{\mathrm{E}}=\mathrm{I}_{\mathrm{C}}+\mathrm{I}_{\mathrm{B}}\).

Step-by-step solution

Recall Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law states that the sum of currents entering a junction is equal to the sum of currents leaving the junction. We will apply KCL at the transistor junction, where the base current (\(\mathrm{I}_{\mathrm{B}}\)), collector current (\(\mathrm{I}_{\mathrm{C}}\)), and emitter current (\(\mathrm{I}_{\mathrm{E}}\)) meet.

Apply KCL to the transistor junction

Applying KCL to the transistor junction, we can write: \(\mathrm{I}_{\mathrm{E}}\) (incoming) = \(\mathrm{I}_{\mathrm{C}}\) (outgoing) + \(\mathrm{I}_{\mathrm{B}}\) (outgoing)

Compare the obtained relation with the given options

Rewriting the obtained relation, we have: \(\mathrm{I}_{\mathrm{E}}=\mathrm{I}_{\mathrm{C}}+\mathrm{I}_{\mathrm{B}}\) Comparing this relation with the given options, we can see that it matches with option (C). Therefore, the correct relation between the transistor currents is: (C) \(\mathrm{I}_{\mathrm{E}}=\mathrm{I}_{\mathrm{C}}+\mathrm{I}_{\mathrm{B}}\)

Key concepts

Kirchhoff's Current Law

Kirchhoff's Current Law (KCL) is a fundamental principle used to analyze complex electrical circuits. It is named after the German physicist Gustav Kirchhoff. KCL is crucial because it helps in predicting how current moves through electrical pathways. The core idea of KCL is elegantly simple: the total current entering a junction (or node) must equal the total current leaving the junction. This means if current flows into a point in a circuit, the same amount of current must flow out to maintain balance.

This principle is based on the law of conservation of charge. If the incoming currents were not equal to the outgoing currents at a node, it would imply that charge is either being created or destroyed, which contradicts the conservation laws.

In the context of a transistor, considered a key building block in electronics, KCL helps in understanding how the three currents – base, collector, and emitter – interrelate.

Base Current (I_B)

The base current, denoted as \(I_B\), is one of the three essential currents in a transistor. It plays a pivotal role because the base acts as the control gate for the current flowing between the emitter and collector. In most transistors, especially Bipolar Junction Transistors (BJTs), the base current is considerably smaller than the collector and emitter currents. This is because the base-emitter junction is forward biased, allowing electrons to flow easily.

The amount of base current controls the collector current due to the transistor's current amplification capability. This phenomenon means that small changes in \(I_B\) can lead to significant variations in the collector current \(I_C\), affecting the amplifications that transistors are popularly used for.

A practical approach to calculate \(I_B\) in a circuit involves knowing the transistor’s beta (\(\beta\)), which is the current gain, and using the relation \( I_B = \frac{I_C}{\beta} \) provided \(I_C\) is known.

Collector Current (I_C)

The collector current, \(I_C\), is the most significant current in terms of magnitude in a transistor operation, especially in the conductive state of a bipolar junction transistor. It primarily consists of the electrons that flow from the emitter and get collected at the collector terminal. The amount of \(I_C\) dictates the maximum power of a transistor as it usually handles the primary load of the circuit.

In the relation \(I_E = I_C + I_B\) (as per KCL applied to transistor junctions), \(I_C\) represents the majority of the current flow from the emitter to collector, making the collector current integral for the overall function of a transistor.

Engineers often calculate \(I_C\) to design circuits that use transistors for amplification. It can also be approximated by \(I_C = \beta \times I_B\), where \(\beta\) is the DC current gain of the transistor, assuming the emitter current \(I_E\) is relatively stable under given conditions.

Emitter Current (I_E)

The emitter current \(I_E\) is crucial because it provides the necessary carriers for the conduction through a transistor. It is considered the input current of the transistor, as it stems from the charge carriers emitted by the transistor's emitter region. Understanding \(I_E\) is pivotal, as it can be seen as the sum of the collector and base currents.

The relation \(I_E = I_C + I_B\) is derived directly from applying KCL at the junction, where these currents converge. This relation shows that the emitter current is the sum of the other two currents, providing insight into the current flow mechanism within the transistor.

In practice, \(I_E\) can be used to compute the other two currents if one of them is given along with a known \(\beta\). For example, knowing \(I_C\) and \(\beta\), you can find \(I_B\) and similarly determine \(I_E\) in circuit analysis and design.