on electrical percolation in rod networks have also been analyzed [@Otten2009; @Otten2011; @Mutiso2012]. The impact of the orientation of the cylinders on percolation behavior was discussed in [@Munson1991]. A detailed review of the effects of aspect ratio, dispersity in filler size and electrical properties, orientation, flexibility and waviness on the percolation behavior of systems of rodlike particles has recently been presented by [@Mutiso2015].

In 2D systems for oriented capped rectangles of length $l$ and width $d$, the value of $V_{ex}$ can be derived from the formulae presented in [@Balberg1984a] $$\label{eq:Vex2D}
V_{ex}=l^2\left[\langle \sin\theta \rangle+4/a+\pi/a^2\right].$$ For random orientations of rectangles, $\langle \sin\theta \rangle=2/\pi$, and in the limit of $a\rightarrow \infty$ we have $V_{ex}=(2/\pi)l^2$.

The following interpolation formulas for the total critical filling fraction of particles at the percolation points have been obtained for randomly oriented ellipses [@Xia1988] $$\label{eq:ellipses}
p_c= 1- (1 + 4y)/(19 + 4y),$$ and rectangles [@Li2013] $$\label{eq:rectangles}
p_c= 1-(1.28 + y)/(6.73 + y).$$ Here, $y = a +1/a$; where $a$ is the aspect ratio.

Considerable attention has been paid to the 2D percolation problem of zero-width rods ($a=\infty$) [@Pike1974; @Balberg1983; @Robinson1983; @Robinson1984; @Li2009; @Dalafi2010; @Mertens2012; @Mietta2014]. An inverse proportionality rule $n_c\propto V^{-1}_{ex}\propto l^{-2}$  has also been confirmed for this system. 