An N-channel E-MOSFET has the following parameters: 

I_D(ON) = 5 mA at V_GS = 10 V and V_GS(th) = 5 V

Calculate its drain current for V_GS = 8 V. 

Explanation:

Correct Option Analysis:

The correct option is:

Option 4: 1.8 mA

We are given an N-channel E-MOSFET with the following parameters:

• ID(ON) = 5 mA at VGS = 10 V
• VGS(th) = 5 V

We need to calculate its drain current (ID) for VGS = 8 V.

The drain current for an E-MOSFET in the saturation region can be calculated using the following equation:

ID = ID(ON) * ((VGS - VGS(th)) / (VGS(ON) - VGS(th)))^2

Given:

• ID(ON) = 5 mA
• VGS(ON) = 10 V
• VGS(th) = 5 V
• VGS = 8 V

Substitute the given values into the equation:

ID = 5 mA * ((8 V - 5 V) / (10 V - 5 V))^2

Calculate the terms inside the parentheses first:

(8 V - 5 V) = 3 V

(10 V - 5 V) = 5 V

Now, substitute these values back into the equation:

ID = 5 mA * (3 V / 5 V)^2

Simplify the fraction:

ID = 5 mA * (0.6)^2

Calculate the square of 0.6:

(0.6)^2 = 0.36

Now, multiply this by 5 mA:

ID = 5 mA * 0.36

ID = 1.8 mA

Therefore, the drain current for VGS = 8 V is 1.8 mA, making option 4 the correct answer.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 3.2 mA

Using the same method, if we substitute the values into the equation:

ID = 5 mA * ((8 V - 5 V) / (10 V - 5 V))^2

ID = 5 mA * (3 V / 5 V)^2

ID = 5 mA * (0.6)^2

ID = 5 mA * 0.36

ID = 1.8 mA

Clearly, the calculation shows that the correct drain current is 1.8 mA and not 3.2 mA, so option 1 is incorrect.

Option 2: 4 mA

Again, using the same method:

ID = 5 mA * ((8 V - 5 V) / (10 V - 5 V))^2

ID = 5 mA * (3 V / 5 V)^2

ID = 5 mA * (0.6)^2

ID = 5 mA * 0.36

ID = 1.8 mA

The calculation confirms that 1.8 mA is the correct value, so option 2 is incorrect as well.

Option 3: 2.6 mA

Using the same method:

ID = 5 mA * ((8 V - 5 V) / (10 V - 5 V))^2

ID = 5 mA * (3 V / 5 V)^2

ID = 5 mA * (0.6)^2

ID = 5 mA * 0.36

ID = 1.8 mA

The calculation clearly shows that 2.6 mA is not the correct drain current, thus option 3 is also incorrect.

Conclusion:

Understanding the operation of an N-channel E-MOSFET and the application of the drain current equation are crucial for correctly identifying the drain current for a given gate-source voltage. By carefully substituting the given values and performing the calculations, we have determined that the correct drain current for VGS = 8 V is 1.8 mA. This confirms that option 4 is the correct answer.