Current Source and Its Characteristics

A current source is an electronic component or circuit that supplies or absorbs electric current which is independent of the voltage across it. In an ideal scenario, a current source delivers a constant current irrespective of the load connected to it. However, practical current sources always possess an internal resistance, which influences their behavior.

For a practical current source, its internal resistance is typically represented as being in parallel with an ideal current source. When a load resistor is connected across this practical current source, the total current generated by the ideal current source splits between its own internal resistance and the connected load resistance. The amount of current that flows through the load determines how "stiff" or "ideal-like" the current source behaves.

• Given Source Current (\(I_s\)): \(2 \, \text{mA}\)
• Given Internal Resistance of the current source (\(R_s\)): \(20 \, \text{M}\Omega\)

Stiff Current Source Definition

A current source is considered "stiff" when its output current remains nearly constant even as the load resistance changes within a certain range. This desirable characteristic is achieved when the internal resistance of the current source is much larger than the load resistance. When the internal resistance is significantly greater, most of the current from the source is directed through the load, making the source behave more like an ideal current source.

A common rule of thumb used to define a stiff current source is that its internal resistance (\(R_s\)) should be at least 100 times greater than the load resistance (\(R_L\)). This criterion ensures that the current flowing through the internal resistance is negligible compared to the current flowing through the load, thus maintaining a stable current to the load.

The condition for a stiff current source is:

\[R_s \ge 100 \times R_L\]

Load Resistance Range Calculation

To determine the maximum load resistance for which the current source can be considered stiff, we need to find the upper limit of \(R_L\) based on the stiffness criterion. We can rearrange the inequality to solve for \(R_L\):

\[R_L \le \frac{R_s}{100}\]

We are provided with the internal resistance \(R_s = 20 \, \text{M}\Omega\). It is important to convert this into Ohms for calculation:

\[R_s = 20 \times 10^6 \, \Omega\]

Now, substitute the value of \(R_s\) into the formula to calculate the maximum permissible load resistance (\(R_{L,max}\)):

\[R_{L,max} = \frac{20 \times 10^6 \, \Omega}{100}\]

\[R_{L,max} = 20 \times 10^4 \, \Omega\]

\[R_{L,max} = 200 \times 10^3 \, \Omega\]

To express this in a more convenient unit, we convert Ohms to kilo-Ohms (\(\text{k}\Omega\)), where \(1 \, \text{k}\Omega = 10^3 \, \Omega\):

\[R_{L,max} = 200 \, \text{k}\Omega\]

Therefore, for the current source to be considered stiff, the load resistance (\(R_L\)) must be less than or equal to \(200 \, \text{k}\Omega\). Since resistance values start from zero, the valid range for the load resistance is from \(0 \, \text{to} \, 200 \, \text{k}\Omega\).

Let's compare this calculated range with the provided options:

Based on our calculation, the load resistance must be from \(0 \, \text{to} \, 200 \, \text{k}\Omega\) for the current source to be stiff. This corresponds to the range presented in the first option.