Question

In a N-P-N transistor circuit, the emitter, collector and base current are respectively \(\mathrm{I}_{E}, I_{C}\) and \(I_{B} .\) The relation between them is (A) \(\mathrm{I}_{\mathrm{C}}<\mathrm{I}_{\mathrm{E}}<\mathrm{I}_{\mathrm{B}}\) (B) \(\mathrm{I}_{\mathrm{B}}<\mathrm{I}_{\mathrm{C}}<\mathrm{I}_{\mathrm{E}}\) (C) \(\mathrm{I}_{\mathrm{B}}>\mathrm{I}_{\mathrm{C}}<\mathrm{I}_{\mathrm{E}}\) (D) \(\mathrm{I}_{\mathrm{B}}>\mathrm{I}_{\mathrm{C}}>\mathrm{I}_{\mathrm{E}}\)

Short answer

The correct relation between the emitter, collector, and base currents in an N-P-N transistor circuit is given by option (B): \(\mathrm{I}_{\mathrm{B}}<\mathrm{I}_{\mathrm{C}}<\mathrm{I}_{\mathrm{E}}\).

Step-by-step solution

Recall the current relation in an N-P-N transistor

In an N-P-N transistor, the emitter current \(\mathrm{I}_{E}\) is the sum of the base current \(I_{B}\) and the collector current \(I_{C}\), i.e., \[\mathrm{I}_{E} = I_{B} + I_{C}.\]

Analyze the options

Now, let's analyze each option to identify which one conforms to the transistor current relation: (A) \(\mathrm{I}_{\mathrm{C}}<\mathrm{I}_{\mathrm{E}}<\mathrm{I}_{\mathrm{B}}\) In this option, the emitter current is greater than the collector current but less than the base current. Thus, this option is not consistent with the relationship: \(\mathrm{I}_{E} = I_{B} + I_{C}\). (B) \(\mathrm{I}_{\mathrm{B}}<\mathrm{I}_{\mathrm{C}}<\mathrm{I}_{\mathrm{E}}\) In this option, the emitter current is larger than the collector current and the base current, and the collector current is larger than the base current. This option is consistent with the relationship: \(\mathrm{I}_{E} = I_{B} + I_{C}\). (C) \(\mathrm{I}_{\mathrm{B}}>\mathrm{I}_{\mathrm{C}}<\mathrm{I}_{\mathrm{E}}\) In this option, the emitter current is larger than the collector current, but the base current is larger than both. Thus, this option is not consistent with the relationship: \(\mathrm{I}_{E} = I_{B} + I_{C}\). (D) \(\mathrm{I}_{\mathrm{B}}>\mathrm{I}_{\mathrm{C}}>\mathrm{I}_{\mathrm{E}}\) In this option, the base current is larger than the collector and emitter currents, and the collector current is larger than the emitter current. Thus, this option is not consistent with the relationship: \(\mathrm{I}_{E} = I_{B} + I_{C}\).

Choose the correct option

From the analysis above, we can conclude that only option (B) is consistent with the current relation in an N-P-N transistor, where \(\mathrm{I}_{\mathrm{B}}<\mathrm{I}_{\mathrm{C}}<\mathrm{I}_{\mathrm{E}}\).

Key concepts

Emitter Current

In a N-P-N transistor, the emitter current, denoted as \(I_E\), is a crucial part of the device's functioning. The emitter is essentially the source of charge carriers, mostly electrons, which are injected into the transistor. From the physical point of view, it can be seen as the current flowing out of the emitter terminal of the transistor.

To understand the magnitude of the emitter current, consider its dependency on other transistor currents:

• \(I_E\) is generally the largest current in a transistor circuit. This is because it is the sum of both the base and collector currents.
• It pushes the charge carriers across the junctions, allowing the transistor to amplify signals and transfer power.

This relationship can be summarized by the equation \( I_E = I_B + I_C \), where \( I_B \) is the base current, and \( I_C \) is the collector current.
Overall, emitter current plays a pivotal role as it defines how much charge is entering the transistor system.

Collector Current

The collector current, \(I_C\), is another fundamental component in an N-P-N transistor. As the name suggests, it collects the charge carriers that have been injected into the collector from the emitter. This terminal is typically connected to a higher voltage, which helps draw electrons (or holes, depending on the type of transistor) to flow through the device.

Characteristics of collector current include:

• It is typically larger than the base current but less than the emitter current.
• Most of the carrier charge reaching the collector comes from the emitter, thus making the collector current mostly a result of emitter action.
• Efficiency of a transistor greatly relies on how effectively the collector can attract these charge carriers.

The collector current is critical in determining the output characteristics of a transistor such as its output power and voltage gain.

Base Current

Base current, represented by \(I_B\), flows into the base terminal of an N-P-N transistor. The base is a thin, middle layer sandwiched between the emitter and collector, and its primary role is to control the transistor's operation.

Key aspects about base current include:

• It is usually the smallest current in the transistor. This is due to the base's small size and high resistivity compared to the emitter and collector.
• Even though \(I_B\) is small, it is crucial for the device to function correctly because it controls the larger collector current for amplification purposes.
• The precise control of the base current is what allows a transistor to work effectively as a switch or an amplifier.

Thus, while base current is small in magnitude, its role in controlling larger currents makes it significant in transistor circuits.

Current Relationship in Transistors

The current relationship in transistors is crucial for understanding how these devices operate. For an N-P-N transistor, the relationship between emitter current \(I_E\), base current \(I_B\), and collector current \(I_C\) can be mathematically expressed as:\[ I_E = I_B + I_C \]
This equation highlights several important points:

• The emitter current is the sum of the base and collector currents, which means \(I_E\) is always the highest.
• This relationship is linear, allowing for predictable behavior of the transistor, necessary for design and analysis of circuits.
• The base current being minimal allows for effective control over larger currents, lending to the transistor's role in amplification.

Understanding this simple relationship is foundational for grasping how transistors can amplify signals, switch, and control electronic circuits efficiently.