When the plate voltage is 36 V , the power delivered in the plate circuit of a diode is 1.0 W . Determine the power delivered if the plate voltage is raised to 49 V . Assume the Langmuir–Child equation holds true.

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 2.2 W

According to the Langmuir-Child equation, the plate current

I_p

is proportional to

V_p^{3/2}

.

I_p = k V_p^{3/2}

The power delivered in the plate circuit is given by:

P = V_p I_p = k V_p^{5/2}

Given

P_1 = 1.0 \text{ W}

at

V_{p1} = 36 \text{ V}

and

V_{p2} = 49 \text{ V}

.

\dfrac{P_2}{P_1} = \left(\dfrac{V_{p2}}{V_{p1}}\right)^{5/2}

P_2 = 1.0 \times \left(\dfrac{49}{36}\right)^{5/2}

P_2 = \left(\left(\dfrac{7}{6}\right)^2\right)^{5/2} = \left(\dfrac{7}{6}\right)^5

P_2 = \dfrac{16807}{7776} \approx 2.16 \text{ W}

Rounding to one decimal place,

P_2 \approx 2.2 \text{ W}

.

When the plate voltage is 36 V , the power delivered in the plate...

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