A capacitor has capacitance 5 μF when its parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness d/2 is inserted between the plates. Capacitance of the capacitor in the presence of slab will b e _____ μF.
Physics · Capacitor · capacitor with dielectric
JEE Mains 25 January 2023 Shift 2 Evening Shift

Question

A capacitor has capacitance 5 μF when its parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness d/2 is inserted between the plates. Capacitance of the capacitor in the presence of slab will b e _____ μF.

Physics · Capacitor · capacitor with dielectric

JEE Mains 25 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

With a dielectric slab of thickness d/2 and air in the remaining d/2, the effective separation is d(eff) = (d/2)/1.5 + d/2 = d/3 + d/2 = 5d/6. Hence C(new) = ε₀A/[5d/6] = (6/5)(ε₀A/d) = (6/5)(5 μF) = 6 μF.