The relation between dynamic plate resistance | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The dynamic plate resistance is defined as $r_p = \frac{dV_p}{dI_p}$.For a vacuum diode in the space charge limited region,the plate current $I_p$

Vedclass · Accepted Answer

$r_p \propto \frac{1}{I_p^{1/3}}$

Vedclass · Answer

(D) The dynamic plate resistance is defined as $r_p = \frac{dV_p}{dI_p}$.For a vacuum diode in the space charge limited region,the plate current $I_p$ is related to the plate voltage $V_p$ by Child's Law: $I_p = K V_p^{3/2}$,where $K$ is a constant.Rearranging for $V_p$,we get $V_p = \left( \frac{I_p}{K} ight)^{2/3}$.Differentiating $V_p$ with respect to $I_p$:$\frac{dV_p}{dI_p} = \frac{d}{dI_p} \left( \frac{I_p^{2/3}}{K^{2/3}} ight) = \frac{1}{K^{2/3}} \cdot \frac{2}{3} I_p^{(2/3 - 1)} = \frac{2}{3 K^{2/3}} I_p^{-1/3}$.Since $r_p = \frac{dV_p}{dI_p}$,we have $r_p = 	ext{constant} \cdot I_p^{-1/3}$.Therefore,$r_p \propto \frac{1}{I_p^{1/3}}$.

The relation between dynamic plate resistance $(r_p)$ of a vacuum diode and plate current $(I_p)$ in the space charge limited region is:

Similar Questions

In the figure,four plate characteristics of a triode at different grid voltages are shown. The difference between successive grid voltages is $1 \ V$. Which curve will have the maximum grid voltage and what is its value?

$A$ triode has a plate resistance of $10 \, k\Omega$ and an amplification factor of $24$. If the input signal voltage is $0.4 \, V$ $(r.m.s.)$ and the load resistance is $10 \, k\Omega$,then the output voltage $(r.m.s.)$ is ...... $V$.

The relation between $I_p$ and $V_p$ for a triode is $I_p = (0.125V_p - 7.5) \text{ mA}$. Keeping the grid potential constant at $1 \text{ V}$,the value of $r_p$ will be . . . . . . $\text{k}\Omega$.

If ${R_p} = 7 \text{ k}\Omega$ and ${g_m} = 2.5 \text{ millimho}$, then on increasing the plate voltage by $50 \text{ V}$, how much must the grid voltage be changed so that the plate current remains the same? (in $V$)

The slope of the anode characteristic and the mutual characteristic of a triode are $0.02 \text{ mA/V}$ and $1 \text{ mA/V}$ respectively. The amplification factor of the valve is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module