Modern Physics Ques 248
- A triode has plate characteristics in the form of parallel lines in the region of our interest. At a grid voltage of $-1$ $ V$ the anode current $I$ (in $mA$ ) is given in terms of plate voltage $V$ by the algebraic relation :
$ I=0.125 A-7.5 $
For grid voltage of $-3 $ $V$, the current at anode voltage of $300 $ $V$ is $5$ $ mA$. Determine the plate resistance $\left(r _p\right)$ transconductance $\left(g _m\right)$ and the amplification factor $(\mu)$ for the triode.
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Answer:
Correct Answer: 248.$(8 k \Omega, 12.5 \times 10^{-3} A / V, 100)$
Solution:
Formula:
- Given, at $V _g=-1 V$
$ \begin{alignedat} & I _p=\left(0.125 V _p-7.5\right) \times 10^{-3} A \\ & \left.\frac{d I _p}{d V _p}\right| _{V _g=-1 \text { volt }}=0.125 \times 10^{-3} A / V \\ & \therefore \quad r _p=\left.\frac{d V _p}{d I _p}\right| _{V _g=-1 \text { volt }}=\frac{1}{0.125 \times 10^{-3}} \Omega \\ & =8 \times 10^{3} \Omega=8 k \Omega \end{aligned} $
From the given equation,
$ \begin{aligned} I _p & =(0.125 \times 300 - 7.5) mA \\ \left(\text { at } V _g\right. & \left.=-1 V \text { and } V _p=300 V\right)=30\ \text{mA} \end{aligned} $
Now,
$ \begin{alignedat} g _m & =\left.\frac{\Delta I _p}{\Delta V _g}\right| _{V _p=\text { constant }} \\ & =\left.\frac{(30-5)}{(-1)-(-3)}\right| _{V _p=300 \text { volt }} \\ & =12.5 \times 10^{-3} A / V \end{aligned} $
Amplification factor $\mu=r_p \times g_m=100$
BETA
