Verified Solution • 2025–26 Session moderate

QJEEM22Ph29d3: JEE Main 2022 Physics - Class 12 JEEM22Ph29d3 Solution: Two metallic plates form a parallel plate capacitor. The…

Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness d2{d \over 2} and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

Multiple Choice Options

  • A 2:01
  • B 1:02
  • C 1:04
  • D 4:01

Step-by-Step Verified Solution

Ceq=ε0Ad−d2+d2k=ε0Ad2=2ε0Ad{C_{eq}} = {{{\varepsilon _0}A} \over {d - {d \over 2} + {d \over {2k}}}} = {{{\varepsilon _0}A} \over {{d \over 2}}} = {{2{\varepsilon _0}A} \over d}

If C=ε0AdC = {{{\varepsilon _0}A} \over d}

⇒Ceq=2C\Rightarrow {C_{eq}} = 2C or CnewCold=21{{{C_{new}}} \over {{C_{old}}}} = {2 \over 1}

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