The input resistance of a silicon transistor is $100\, \Omega$. Base current is changed by $40\, \mu ext{A}$

Question

The input resistance of a silicon transistor is $100\, \Omega$. Base current is changed by $40\, \mu	ext{A}$ which results in a change in collector current by $2	ext{ mA}$. This transistor is used as a common-emitter amplifier with a load resistance of $4	ext{ k}\Omega$. The voltage gain of the amplifier is:

Accepted Answer

1. **Identify Given Data:**
   * Input resistance, $R_{in} = 100\, \Omega$
   * Change in base current, $\Delta I_B = 40\, \mu	ext{A} = 40 	imes 10^{-6}	ext{ A}$
   * Change in collector current, $\Delta I_C = 2	ext{ mA} = 2 	imes 10^{-3}	ext{ A}$
   * Load resistance, $R_L = 4	ext{ k}\Omega = 4000\, \Omega$
2. **Calculate Current Gain ($\beta$):**
   * $\beta = \frac{\Delta I_C}{\Delta I_B} = \frac{2 	imes 10^{-3}}{40 	imes 10^{-6}} = \frac{2000}{40} = 50$
3. **Calculate Voltage Gain ($A_v$):**
   * $A_v = \beta 	imes \frac{R_L}{R_{in}} = 50 	imes \frac{4000}{100} = 50 	imes 40 = 2000$

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