1.

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be:

A. \({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_3}} \right)\left( {{{\rm{K}}_2} + {{\rm{K}}_4}} \right)}}{{{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}}}\)
B. \({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_2}} \right)\left( {{{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}{{2\left( {{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}\)
C. \({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_2}} \right)\left( {{{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}{{{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}}}\)
D. \({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_4}} \right)\left( {{{\rm{K}}_2} + {{\rm{K}}_3}} \right)}}{{2\left( {{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}\)
Answer» D. \({\rm{K}} = \frac{{\left( {{{\rm{K}}_1} + {{\rm{K}}_4}} \right)\left( {{{\rm{K}}_2} + {{\rm{K}}_3}} \right)}}{{2\left( {{{\rm{K}}_1} + {{\rm{K}}_2} + {{\rm{K}}_3} + {{\rm{K}}_4}} \right)}}\)


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