Concepts Of Physics MCQ Edition [Volume 2]PhysicsCapacitors
The following operations can be carried out on a capacitor: X – attach the capacitor to a battery of emf E . Y – disconnect the battery. Z – reconnect the battery with reversed polarity. W – introduce a dielectric slab into the capacitor.
Options
- AThe electric energy stored in the capacitor is higher after the sequence WXY compared to the sequence XYW.
- BThe electric field inside the capacitor after the sequence XW is identical to that after WX.
- CThe charge present on the capacitor is larger following the sequence XWY than after the sequence XYW.
- DDuring the sequence XYZ (performing X, then Y, then Z), the stored electric energy stays the same and no therm
Correct answer
C. The charge present on the capacitor is larger following the sequence XWY than after the sequence XYW.
Step-by-step solution
Let the initial capacitance be C and the dielectric constant of the slab be K > 1 . For option 1: Sequence WXY: Introducing the dielectric (W) makes the capacitance KC . Attaching the battery (X) charges it to a potential E , giving stored energy U₁ = 1 2 KC E ^2 . Disconnecting the battery (Y) keeps the charge and energy constant. Thus, U₁ = 1 2 KC E ^2 . Sequence XYW: Attaching the battery (X) charges the capacitor to Q = C E . Disconnecting the battery (Y) keeps the charge constant at C E . Introducing the diele