The correct answer is option 'B', which states that the value of the transistor's resistance in a series voltage regulator is determined by the base current. Let's understand why this is the case.

Overview of a Series Voltage Regulator:
A series voltage regulator is a type of voltage regulator circuit that uses a transistor to maintain a constant output voltage despite variations in the input voltage or load current. It consists of a series pass transistor, a voltage reference, and feedback components.

Role of the Transistor:
The main component in a series voltage regulator is the transistor, which acts as a variable resistor in the circuit. Its resistance value determines the amount of voltage drop across it, thereby regulating the output voltage.

Explanation:
To understand why the value of the transistor's resistance is determined by the base current, let's consider the working principle of a series voltage regulator.

1. Voltage Reference:
The series voltage regulator uses a voltage reference, typically a Zener diode or a voltage divider network, to provide a stable reference voltage.

2. Base-Emitter Junction:
The base-emitter junction of the transistor is forward biased using the reference voltage. This biasing establishes a constant voltage across the base-emitter junction.

3. Base Current:
The base current is controlled by the feedback components, such as resistors and capacitors, connected between the output and the base of the transistor. These components compare the output voltage with the reference voltage and adjust the base current accordingly.

4. Transistor Operation:
As the base current increases, the transistor enters the active region of operation. In this region, the transistor acts as a variable resistor, allowing a controlled amount of current to flow from the collector to the emitter.

5. Voltage Drop:
The voltage across the transistor is the difference between the input voltage and the output voltage. This voltage drop is directly proportional to the base current. As the base current increases, the resistance of the transistor decreases, resulting in a larger voltage drop.

6. Output Voltage Regulation:
By adjusting the base current, the resistance of the transistor is controlled, which, in turn, regulates the voltage drop and maintains a constant output voltage. If the output voltage increases, the feedback components decrease the base current, increasing the transistor's resistance and reducing the voltage drop. Similarly, if the output voltage decreases, the feedback components increase the base current to decrease the transistor's resistance and increase the voltage drop.

In conclusion, the value of the transistor's resistance in a series voltage regulator is determined by the base current. By controlling the base current, the resistance of the transistor is adjusted, which regulates the voltage drop across it and maintains a constant output voltage.