Question

In a transistor, if the emitter and collector currents are respectively 2 mA and 1.95 mA, then the base current is

• A. 50 $\mu$A
• B. 0.05 $\mu$A
• C. 50 mA
• D. 5 mA

Hint:

In a transistor, the emitter current is the sum of the base and collector currents ($I_E = I_B + I_C$). This fundamental relationship is crucial for solving problems involving transistor currents. Remember to ensure all current values are in consistent units (e.g., all in mA or all in $\mu$A) before performing calculations.

Answer 1

The Correct Option is A

Step 1: Understand the Fundamental Relationship of Currents in a Transistor
In a bipolar junction transistor (BJT), the emitter current ($I_E$) is the sum of the base current ($I_B$) and the collector current ($I_C$). This relationship is based on Kirchhoff's current law applied to the transistor. The fundamental current relationship is given by: \[ I_E = I_B + I_C \] Our goal is to find the base current ($I_B$). Rearranging the formula: \[ I_B = I_E - I_C \] Step 2: Identify the Given Current Values
Emitter current: $I_E = 2 \text{ mA}$ Collector current: $I_C = 1.95 \text{ mA}$ Step 3: Compute the Base Current
Substitute the given values into the derived formula for $I_B$: \[ I_B = 2 \text{ mA} - 1.95 \text{ mA} \] \[ I_B = 0.05 \text{ mA} \] Step 4: Convert the Result to the Required Units (if necessary)
The options are given in $\mu$A and mA. It's often convenient to convert mA to $\mu$A for comparison, as $1 \text{ mA} = 1000 \text{ } \mu\text{A}$. \[ I_B = 0.05 \text{ mA} = 0.05 \times 1000 \text{ } \mu\text{A} \] \[ I_B = 50 \text{ } \mu\text{A} \] Step 5: Analyze the Options
\begin{itemize} \item Option (1): 50 $\mu$A. Correct, as it matches our calculated value of $I_B$. \item Option (2): 0.05 $\mu$A. Incorrect (this is $0.05 \text{ mA}$ not $0.05 \text{ } \mu\text{A}$). \item Option (3): 50 mA. Incorrect. \item Option (4): 5 mA. Incorrect. \end{itemize}