Show that the dynamic plate resistance of a diode is `2V/3i` where `V` and `i` are the plate voltage and the plate current respectively. Assume Langmuir-Child equation to hold.

Explanation

To show that the dynamic plate resistance \( R_d \) of a diode is given by the formula \( R_d = \frac{2V}{3i} \), where \( V \) is the plate voltage and \( i \) is the plate current, we will use the Langmuir-Child equation. The steps are as follows:

### Step 1: Write the Langmuir-Child Equation
The Langmuir-Child equation relates the plate current \( i \) to the plate voltage \( V \) and is given by:
\[ i = C V^{\frac{3}{2}} \]
where \( C \) is a constant.
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