Answer
Verified
389.1k+ views
Hint: The constant $\alpha $ of a transistor is the ratio of the collector current to the emitter current while the constant $\beta $ of the transistor is the ratio of the collector current to the base current. The base current is lesser than the collector current which is lesser than the emitter current.
Formula used:
$\alpha =\dfrac{{{I}_{C}}}{{{I}_{E}}}$
$\beta =\dfrac{{{I}_{C}}}{{{I}_{B}}}$
Complete step by step answer:
The ratio of the collector current ${{I}_{C}}$ to the emitter current ${{I}_{E}}$ in a transistor is represented by the constant $\alpha $. Therefore, mathematically,
$\alpha =\dfrac{{{I}_{C}}}{{{I}_{E}}}$ -----(1)
In a transistor, the emitter current ${{I}_{E}}$ is the sum of the base current ${{I}_{B}}$ and the collector current ${{I}_{C}}$.
Therefore, obviously it can be said that ${{I}_{E}}>{{I}_{C}}$. Using this relation in (1), we can say that
$\alpha =\dfrac{{{I}_{C}}}{{{I}_{E}}}<1$
The ratio of the collector current ${{I}_{C}}$ to the base current ${{I}_{B}}$ in a transistor is represented by the constant $\beta $. Therefore, mathematically,
$\beta =\dfrac{{{I}_{C}}}{{{I}_{B}}}$ ------(2)
Also, the base current ${{I}_{B}}$ in a transistor is much smaller than both the emitter current ${{I}_{E}}$ and the collector current ${{I}_{C}}$. Therefore, mathematically, ${{I}_{B}}<{{I}_{C}}$.
Using this relation in (2), it can be concluded that
$\beta =\dfrac{{{I}_{C}}}{{{I}_{B}}}>1$
Therefore, we have found out that $\alpha <1$ and $\beta >1$ for a transistor.
Therefore, the correct option is $D)\text{ }\beta >1;\alpha <1$.
Note: Students should not get confused between the ratios $\alpha $ and $\beta $ of a semiconductor. In fact, the above-obtained result that $\alpha $ is less than one and $\beta $ is greater than one serves as a help to students in recalling the formulae in other problems if they keep in mind that the base current is smaller than the collector current which is in turn smaller than the emitter current in the transistor.
Formula used:
$\alpha =\dfrac{{{I}_{C}}}{{{I}_{E}}}$
$\beta =\dfrac{{{I}_{C}}}{{{I}_{B}}}$
Complete step by step answer:
The ratio of the collector current ${{I}_{C}}$ to the emitter current ${{I}_{E}}$ in a transistor is represented by the constant $\alpha $. Therefore, mathematically,
$\alpha =\dfrac{{{I}_{C}}}{{{I}_{E}}}$ -----(1)
In a transistor, the emitter current ${{I}_{E}}$ is the sum of the base current ${{I}_{B}}$ and the collector current ${{I}_{C}}$.
Therefore, obviously it can be said that ${{I}_{E}}>{{I}_{C}}$. Using this relation in (1), we can say that
$\alpha =\dfrac{{{I}_{C}}}{{{I}_{E}}}<1$
The ratio of the collector current ${{I}_{C}}$ to the base current ${{I}_{B}}$ in a transistor is represented by the constant $\beta $. Therefore, mathematically,
$\beta =\dfrac{{{I}_{C}}}{{{I}_{B}}}$ ------(2)
Also, the base current ${{I}_{B}}$ in a transistor is much smaller than both the emitter current ${{I}_{E}}$ and the collector current ${{I}_{C}}$. Therefore, mathematically, ${{I}_{B}}<{{I}_{C}}$.
Using this relation in (2), it can be concluded that
$\beta =\dfrac{{{I}_{C}}}{{{I}_{B}}}>1$
Therefore, we have found out that $\alpha <1$ and $\beta >1$ for a transistor.
Therefore, the correct option is $D)\text{ }\beta >1;\alpha <1$.
Note: Students should not get confused between the ratios $\alpha $ and $\beta $ of a semiconductor. In fact, the above-obtained result that $\alpha $ is less than one and $\beta $ is greater than one serves as a help to students in recalling the formulae in other problems if they keep in mind that the base current is smaller than the collector current which is in turn smaller than the emitter current in the transistor.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE