Question

For a common-emitter transistor, input current is \[5\,\mu A\]. Circuit is operated at load resistance of \[10\,k\Omega \]. The voltage across collector emitter will be
A. 5 V
B. 10 V
C. 12.5 V
D. 7.5 V

Answer 1

Hint: Using the relation between amplification factor, collector current and base current calculate the collector current. Use the formula for voltage across the collector and emitter to determine the collector emitter current.

Complete step by step answer:
The current amplification factor is given as,
\[\beta = \dfrac{{{I_C}}}{{{I_B}}}\]
Here, \[{I_C}\] is the collector current and \[{I_B}\] is the base current.
The voltage across collector emitter is given as,
\[{V_{CE}} = {R_L}{I_C}\]
Here, \[{R_L}\] is the load resistor across the output of the collector emitter.

We know that the current amplification factor is defined as the ratio of collector current to the base current.
\[\beta = \dfrac{{{I_C}}}{{{I_B}}}\]
Here, \[{I_C}\] is the collector current and \[{I_B}\] is the base current.
We know that in common emitter configuration, the input current is given to the base of the transistor. Therefore, the base current is \[{I_B} = 5\,\mu A\].
From the above equation, we can calculate the collector current as follows,
\[{I_C} = \beta {I_B}\]
We substitute 100 for \[\beta \] and \[5\,\mu A\] for \[{I_B}\] in the above equation.
\[{I_C} = \left( {100} \right)\left( {5 \times {{10}^{ - 6}}A} \right)\]
\[ \Rightarrow {I_C} = 5 \times {10^{ - 4}}\,A\]
\[ \Rightarrow {I_C} = 0.5\,mA\]
We have the voltage across collector emitter is given as,
\[{V_{CE}} = {R_L}{I_C}\]
Here, \[{R_L}\] is the load resistor across the output of the collector emitter.
We substitute \[10\,k\Omega \] for \[{R_L}\] and \[0.5\,mA\] for \[{I_C}\] in the above equation.
\[{V_{CE}} = \left( {10 \times {{10}^3}\Omega } \right)\left( {0.5 \times {{10}^{ - 3}}A} \right)\]
\[ \Rightarrow {V_{CE}} = 5\,V\]

So, the correct answer is “Option A”.

Note:
The amplification factor or current gain \[\beta \] represents the increase in collector current in terms of base current. While solving the question relating the output of transistors, students should know the relation between collector current, base current and emitter current, \[{I_E} = {I_C} + {I_B}\]. The voltage across the collector-emitter is the change in the output voltage between collector and emitter.