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 \(\mathrm{I}_{\mathrm{B}}<\mathrm{I}_{\mathrm{C}}<\mathrm{I}_{\mathrm{E}}\).