If an emitter current is changed by $4 mA ,$ the collector current changes by $3.5 mA$. The value of $\beta$ will be
- 7
- 0.5
- 0.875
- 3.5
The Correct Option is A
Solution and Explanation
To find the value of $\beta$ in a bipolar junction transistor (BJT), we use the relationship between the emitter current ($I_E$), base current ($I_B$), and collector current ($I_C$). The formula is given by:
$I_E = I_C + I_B$
The current gain $\beta$ is defined as the ratio of the collector current to the base current:
$\beta = \frac{I_C}{I_B}$
Since $I_B = I_E - I_C$, we can substitute this into the equation for $\beta$:
$\beta = \frac{I_C}{I_E - I_C}$
Given that an increase in the emitter current by $4 \, \text{mA}$ results in an increase in the collector current by $3.5 \, \text{mA}$, the changes in respective currents are:
- Change in $I_E$: $\Delta I_E = 4 \, \text{mA}$
- Change in $I_C$: $\Delta I_C = 3.5 \, \text{mA}$
Assuming the transistor is operating in active mode, and the changes in current are proportionate, the change in equations can be used:
$\Delta I_E = \Delta I_C + \Delta I_B$
Using the known values:
$4 \, \text{mA} = 3.5 \, \text{mA} + \Delta I_B$
Rearranging gives:
$\Delta I_B = 4 \, \text{mA} - 3.5 \, \text{mA} = 0.5 \, \text{mA}$
Now we can find $\beta$:
$\beta = \frac{\Delta I_C}{\Delta I_B} = \frac{3.5 \, \text{mA}}{0.5 \, \text{mA}} = 7$
Thus, the correct answer is 7.
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Concepts Used:
Semiconductors
Semiconductors are a crystalline solid materials, whose electrical conductivity lies between a conductor and an insulator. Semiconductors are mainly used in the manufacturing of electronic devices like capacitors, transistors, diodes, Integrated circuits, etc.
Properties of Semiconductor:
- Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
- Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
- Lesser power losses.
Uses of Semiconductor:
- Semiconductors are widely used in manufacturing electronics devices like transistors, diodes, sensors, integrated circuits.
- Semiconductors are widely used in all electronic devices, like mobile phones, digital cameras, communication devices, trains, ATMs, etc.