For a given transistor amplifier circuit in CE configuration $$V_{CC} = 1$$ V, $$R_C = 1$$ k$$\Omega$$, $$R_b = 100$$ k$$\Omega$$ and $$\beta = 100$$. Value of base current $$I_b$$ is

First, calculate the maximum possible collector current ($$I_C$$) that can flow through the collector resistor $$R_C$$ from the given supply voltage $$V_{CC}$$:

$$I_C = \frac{V_{CC}}{R_C} = \frac{1\ \text{V}}{1\ \text{k}\Omega} = \frac{1}{1000}\ \text{A} = 10^{-3}\ \text{A} = 1\ \text{mA}$$

The relationship between the collector current and the base current ($$I_b$$) is given by the current amplification factor $$\beta$$:   $$I_C = \beta I_b$$

$$1\ \text{mA} = 100 \times I_b$$ $$\implies$$ $$I_b = \frac{1\ \text{mA}}{100} = 0.01\ \text{mA}$$

$$I_b = 0.01 \times 1000\ \mu\text{A} = 10\ \mu\text{A}$$