An NPN transistor has beta value of 200. Calculate the base current required to switch a resistive load of 4mA. Also find emitter current and collector to emitter gain.
The Correct Answer and Explanation is :
To solve this problem, we need to calculate the base current required to switch a load with a collector current of 4 mA using an NPN transistor with a beta value (β) of 200. Additionally, we will calculate the emitter current and the collector-to-emitter gain.
Step 1: Calculating the Base Current (I_B)
The beta value (β) of a transistor is defined as the ratio of the collector current (I_C) to the base current (I_B). It is given by the equation:
[ \beta = \frac{I_C}{I_B} ]
Rearranging this formula to solve for I_B:
[ I_B = \frac{I_C}{\beta} ]
Given I_C = 4 mA and β = 200, the base current I_B is:
[ I_B = \frac{4 \text{ mA}}{200} = 0.02 \text{ mA} ]
Step 2: Calculating the Emitter Current (I_E)
The emitter current in an NPN transistor is the sum of the collector current and the base current:
[ I_E = I_C + I_B ]
Given I_C = 4 mA and I_B = 0.02 mA:
[ I_E = 4 \text{ mA} + 0.02 \text{ mA} = 4.02 \text{ mA} ]
Step 3: Calculating the Collector-to-Emitter Gain (α)
The collector-to-emitter current gain (α) is defined as the ratio of the collector current to the emitter current:
[ \alpha = \frac{I_C}{I_E} ]
Given I_C = 4 mA and I_E = 4.02 mA:
[ \alpha = \frac{4 \text{ mA}}{4.02 \text{ mA}} \approx 0.995 ]
Explanation
The base current (I_B) required is quite small compared to the collector current due to the high beta value of the transistor, illustrating the transistor’s ability to amplify a small base current into a much larger collector current. This property is fundamental to the operation of transistors in switching and amplification roles. The emitter current (I_E) being slightly higher than the collector current reflects the contribution of the base current to the total current flowing through the emitter. Finally, the collector-to-emitter gain (α) being slightly less than 1 is typical, as it represents the fraction of the emitter current that is due to the collector.
Image Generation
Now, let’s generate a simple diagram illustrating these transistor currents and gains.
Here’s an illustration of an NPN transistor that shows the base, collector, and emitter currents along with the beta value and collector-to-emitter gain. This diagram should help visually explain the relationships between the different currents and transistor parameters discussed.
