Question

In a common emitter amplifier, the voltage gain and the current amplification factor are \(400\) and \(160\) respectively. If the output resistance of the amplifier is \(2500\,\Omega\), then its input resistance is

• A. \(1\,\text{k}\Omega\)
• B. \(6.25\,\text{k}\Omega\)
• C. \(1.25\,\text{k}\Omega\)
• D. \(2\,\text{k}\Omega\)

Hint:

For a transistor amplifier, \[ \boxed{ A_v=A_i\frac{R_o}{R_i}. } \] Thus, \[ \boxed{ R_i=\frac{A_iR_o}{A_v}. } \]

Answer 1

The Correct Option is A

Step 1: Use the relation between gains and resistances. For a common emitter amplifier, \[ A_v=A_i\frac{R_o}{R_i}, \] where \[ A_v=400,\qquad A_i=160,\qquad R_o=2500\,\Omega. \]

Step 2: Calculate the input resistance. Rearranging, \[ R_i=\frac{A_iR_o}{A_v}. \] Substituting the given values, \[ R_i = \frac{160\times2500}{400} = 1000\,\Omega. \] Therefore, \[ R_i=1\,\text{k}\Omega. \] Hence, \[ \boxed{R_i=1\,\text{k}\Omega.} \] Therefore, the correct option is \(\boxed{(A)}\).