When 60 volts are applied across a diode tube, a plate current of 10 mA is obtained. Assuming that the Langmuir–Child equation i_p V_p^ 3/2 is valid, determine the dynamic resistance r_p in this operating condition.

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Quantrex Academy · Accepted Answer

Correct answer: C. 4000

According to the Langmuir-Child equation, the plate current is given by:

i_p = k V_p^{3/2}

Differentiating with respect to

V_p

, we get:

\dfrac{di_p}{dV_p} = \dfrac{3}{2} k V_p^{1/2}

Multiplying and dividing by

V_p

gives:

\dfrac{di_p}{dV_p} = \dfrac{3}{2} \dfrac{k V_p^{3/2}}{V_p} = \dfrac{3}{2} \dfrac{i_p}{V_p}

The dynamic resistance

r_p

is the reciprocal of this derivative:

r_p = \dfrac{dV_p}{di_p} = \dfrac{2}{3} \dfrac{V_p}{i_p}

Substituting the given values

V_p = 60 \text{ V}

and

i_p = 10 \text{ mA} = 10 \times 10^{-3} \text{ A}

:

r_p = \dfrac{2}{3} \times \dfrac{60}{10 \times 10^{-3}}

r_p = \dfrac{2}{3} \times 6000 = 4000 \Omega

When 60 volts are applied across a diode tube, a plate current of...

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