Question

The output characteristics of a transistor is shown in the figure. When \[{V_{CE}}\] is 10V and \[{I_C}\]= 4.0 mA, then the value of \[{\beta _{ac}}\] is __________.

Answer 1

Hint:A transistor is defined as a semiconductor device used to conduct an electric current or electric voltage. For a transistor, the three terminals are base, collector and emitter. When we combine the expressions for \[\alpha \] and \[\beta \] the mathematical relationship between these parameters then we get the current gain of the transistor. By using the relation, we can find the value for \[\beta \].

Formula used:
The mathematical relationship between these parameters can be given as:
\[\alpha = \dfrac{{{I_C}}}{{{I_E}}}\] and \[\beta = \dfrac{{{I_C}}}{{{I_B}}}\]
\[\Rightarrow {I_C} = \alpha {I_E} = \beta {I_B}\]
As \[\alpha = \dfrac{\beta }{{\beta + 1}}\]
\[\beta = \dfrac{\alpha }{{1 - \alpha }}\]
\[{I_E} = {I_C} + {I_B}\]
Where \[{I_C}\] is the current in the collector terminal, \[{I_B}\] is the current in the base terminal and \[{I_E}\] is the current in the emitter terminal.

Complete step by step solution:
A transistor can also use a small signal which is applied between one pair of its terminals to control a large signal at the other pair of terminals. This property is known as gain. A stronger output signal can produce a voltage as well as a current which is dependable on a weaker input signal.
\[\beta = \dfrac{{\Delta {I_c}}}{{\Delta {I_B}}}\]
Substituting the values
\[\Delta {I_B} = 30 - 20{I_C} = 4\,mA\]
\[\Rightarrow \Delta {I_C} = 4.5 - 3 = 1.5\,mA\]
Now \[\beta = \dfrac{{1.5 \times {{10}^{ - 3}}}}{{10 \times {{10}^{ - 6}}}}\]
\[\therefore \beta = 150\]

Therefore, the value of \[{\beta _{ac}}\] is 150.

Note: In physics, for any transistor the graph shows the relationships between the current(I) and the voltage (V) for any configuration is known as transistor characteristics. The current transfer properties curve can define the variation of output current to the input current by keeping the output voltage constant. There are three transistor circuit configurations. These are Common Emitter Transistor, Common Base Transistor and Common Collector Transistor.