\(V_{o}=2 \mathrm{V}, R_{B}=1 \mathrm{k} \Omega=1 \times 10^{3} \Omega, \beta=100\)

Output voltage, \(V_{o}=I_{c} R_{c}\)

or \(I_{C}=\frac{V_{o}}{R_{C}}=\frac{2 \mathrm{V}}{2 \times 10^{3} \Omega}=10^{-3} \mathrm{A}=1 \mathrm{mA}\)

As \(\beta=\frac{I_{C}}{I_{B}}\) or \(I_{B}=\frac{I_{C}}{\beta} \quad\) or \(\quad I_{B}=\frac{10^{-3} \mathrm{A}}{100}=10^{-5} \mathrm{A}\)

Input voltage, \(V_{i}=I_{B} R_{B}=\left(10^{-5} \mathrm{A}\right)\left(1 \times 10^{3} \Omega\right)\)

\(=10^{-2} \mathrm{V}=10 \mathrm{mV}\)