Three identical thin metal plates  each of area A are arranged parallel to each other with separation d between adjacent plates and the outer plates are connected through a high resistance R as shown in the figure. A charge Q is given to the middle plate and then the middle plate is quickly shifted towards one of the outer plates by a distance d/2. The amount of heat will be dissipated in the resistor after this shift is  $\frac{Q^{2}d}{\left(4x\right){\epsilon }_{0}A}$ (Neglect gravity and assume free space conditions). The value of ‘x’ is_______.