First slide

Transistor

Question

In a common emitter transistor, $β = 100$ and transconductance $(g_{m} = \frac{∆ I_{C}}{∆ V_{B E}})$ is $0.2 {(ohm)}^{- 1}$ . Then its input resistance is

Easy

A

$1000 Ω$
B

$800 Ω$
C

$1500 Ω$
D

$500 Ω$

Solution

$\begin{array}{l} g_{m} = \frac{Δ I_{C}}{Δ V_{B E}} = \frac{Δ I_{C}}{Δ I_{B}} . \frac{Δ I_{B}}{Δ V_{B E}} = β \frac{1}{R i} \\ ∴ R_{i} = \frac{β}{g_{m}} = \frac{100}{0.2} = 500 Ω \end{array}$

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