A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of thickness 2 mm, and maintaining the connections to the terminals of the battery, it is found that the capacitor draws 25% more charge from the battery. The dielectric constant of mica is

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(2) 2.0. The battery stays connected, so V is fixed and (Q')/Q=(C')/C=1.25. With a partially filling slab, C'=(ε₀A)/(d-t+t/K) while C=(ε₀A)/d, so (C')/C=d/(d-t+t/K). 5/(3+2/K)=1.25⇒ 3+2/K=5/(1.25)=4. 2/K=1, so K=2.0.

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of thickness 2 mm, and maintaining the connections to the terminals of the battery, it is found that the capacitor draws 25% more charge from the battery. The dielectric constant of mica is

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