A certain JFET has an I_Gss of -2 nA for V_GS = -20 V. Determine the input resistance.

Explanation:

To determine the input resistance of a JFET given the gate-source leakage current (IGss) and the gate-source voltage (VGS), we can use Ohm's Law. The input resistance (Rin) can be found using the formula:

Rin = VGS / IGss

Given:

• IGss = -2 nA (nanoamperes) = -2 × 10^-9 A
• VGS = -20 V (volts)

Note that the negative signs indicate the direction of current and voltage but do not affect the magnitude of the resistance calculation. We can ignore the negative signs for the purpose of calculating the resistance.

Substituting the given values into the formula:

Rin = VGS / IGss

Rin = 20 V / 2 × 10^-9 A

Rin = 20 / 2 × 10^9

Rin = 10 × 10^9 ohms

Rin = 10 GΩ (gigaohms)

Since 1 GΩ = 1000 MΩ (megaohms), we can convert the result to megaohms:

Rin = 10 × 1000 MΩ

Rin = 10000 MΩ

Therefore, the correct input resistance is 10000 MΩ.

Correct Option Analysis:

The correct option is:

Option 3: 10000 MΩ

This option correctly represents the input resistance of the JFET based on the given values of IGss and VGS.

Additional Information

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

Option 1: 1000 MΩ

This option is incorrect because it underestimates the input resistance. The calculation clearly shows that the input resistance is much higher than 1000 MΩ.

Option 2: 10000 kΩ

This option is also incorrect. Although 10000 kΩ is equal to 10 MΩ, it still underestimates the input resistance by a factor of 1000.

Option 4: 1000 kΩ

This option is incorrect as well. 1000 kΩ is equal to 1 MΩ, which is significantly lower than the calculated input resistance of 10000 MΩ.

Conclusion:

In summary, the input resistance of the JFET is determined by the ratio of the gate-source voltage to the gate-source leakage current. The calculated input resistance of 10000 MΩ matches option 3, making it the correct choice. Understanding the principles of Ohm's Law and the conversion between different units of resistance is essential for accurately solving such problems.