Capacitors

JEE Main level, single correct, medium

108 of 180

Question 108 of 180

A parallel plate capacitor is of area 6cm26c{m}^{2} and a separation 3mm.3mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant K1=10,K2=12{K}_{1}=10,{K}_{2}=12 and K3=14.{K}_{3}=14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be:

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Answer: (D) 1212

C=∈0AdC=\dfrac{{\in }_{0}A}{d}

C1=K1∈0A3d=K1C3{C}_{1}=\dfrac{{K}_{1}{\in }_{0}A}{3d}=\dfrac{{K}_{1}C}{3}

C2=K2C3{C}_{2}=\dfrac{{K}_{2}C}{3}

C3=K3C3{C}_{3}=\dfrac{{K}_{3}C}{3}

Ceq=KeqC=C3(K1+K2+K3){C}_{eq}={K}_{eq}C=\dfrac{C}{3}({K}_{1}+{K}_{2}+{K}_{3})

Keq=K1+K2+K33=363=12{K}_{eq}=\dfrac{{K}_{1}+{K}_{2}+{K}_{3}}{3}=\dfrac{36}{3}=12

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