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Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Current through Gases

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.

Options

  1. A1.9 W
  2. B2.2 W
  3. C1.4 W
  4. D1.6 W

Correct answer

B. 2.2 W

Step-by-step solution

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 P₁ = 1.0 W at V_ p1 = 36 V and V_ p2 = 49 V . P₂ P₁ = ( V_ p2 V_ p1 )^ 5/2 P₂ = 1.0 ( 49 36 )^ 5/2 P₂ = ( ( 7 6 )^2 )^ 5/2 = ( 7 6 )^5 P₂ = 16807 7776 2.16 W Rounding to one decimal place, P₂ 2.2 W .

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