A polymer matrix composite is reinforced with long continuous ceramic fibers aligned in one direction. The young's moduli of the matrix and fibers are Em and Er respectively and the volume fraction of the fibers is f. Assuming iso-stress condition, Young's modulus of the composite Ec in a direction perpendicular to the length of fibers, is given by the expression

A. Ec = (1 - f) E_m + f E_f

B. Ec = f Em + (1 - f) Er

C. $$\frac{1}{{Ec}} = \frac{{\left( {1 - f} \right)}}{{{E_m}}} + \frac{f}{{Ef}}$$

D. $$\frac{1}{{Ec}} = \frac{f}{{{E_m}}} + \frac{{\left( {1 - f} \right)}}{{Ef}}$$

Answer: Option C