Introduction:
In this question, we are asked to determine the effect of increased values of resistance (Rs) on the voltage between the gate and source (Vgs) in a circuit. We are given four options to choose from, and the correct answer is option 'B' - Vgs decreases.

Explanation:
To understand why Vgs decreases when the resistance (Rs) increases, let's consider the basic operation of a field-effect transistor (FET).

Field-Effect Transistor (FET):
A field-effect transistor is a type of transistor that uses an electric field to control the flow of current. It has three terminals: the source (S), the drain (D), and the gate (G). The voltage between the gate and source (Vgs) determines the conductivity of the FET.

Effect of Rs on Vgs:
When the resistance (Rs) increases in a circuit, it means there is a higher voltage drop across Rs. This higher voltage drop reduces the voltage available at the source terminal of the FET. As a result, the voltage between the gate and source (Vgs) decreases.

Reasoning:
The reason for this decrease in Vgs can be understood by considering the voltage divider rule. The voltage divider rule states that the voltage across a resistor in a series circuit is proportional to its resistance value compared to the total resistance in the circuit.

In this case, Rs is in series with the source terminal of the FET. When Rs increases, it contributes a larger portion of the total resistance in the circuit. As a result, the voltage drop across Rs increases, causing a decrease in the voltage available at the source terminal.

Since Vgs is the voltage between the gate and source terminals, a decrease in the source voltage leads to a decrease in Vgs.

Conclusion:
In conclusion, when the resistance (Rs) increases in a circuit, the voltage between the gate and source (Vgs) of a field-effect transistor (FET) decreases. This can be explained by the voltage divider rule, where an increase in Rs leads to a higher voltage drop across it, reducing the voltage available at the source terminal and consequently decreasing Vgs.