A parallel plate capacitor has a dielectric slab in it. The slab just fills the space inside the capacitor. The capacitor is charged by a battery and the battery is disconnected. Now the slab is started to pull out uniformly at t = 0. If at time t, capacitance of the capacitor is C, potential difference across plate is V, and energy stored in it is U, then which of the following graphs are correct ?

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is A, B, C, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Capacitance of capacitor is $S = C_{0} =$ $\frac{k \in_{0} a . L}{d}$

$C = \frac{\in_{0} a x}{d} + \frac{k \in_{0} a (L - x)}{d}$

C = $\frac{a \in_{0}}{d} [x + k (L - x)]$ = $\frac{a \in_{0}}{d} [k L - (k - 1) x]$ = $\frac{a \in_{0}}{d} [k L - (k - 1) v t]$

So, C decreases linearly with time
Charge on capacitor $Q = C_{0} V_{0} =$ $\frac{k \in_{0} a L}{d}$ $V_{0} = c o n s t a n t .$
Potential difference across plate is

V = $\frac{Q}{C} = \frac{C_{0} V_{0}}{C}$ $\Rightarrow$ V $\infty$ $\frac{1}{C}$

$V = \frac{V_{0}}{\frac{a \in_{0}}{d} [k L - (k - 1) v t]}$

Potential energy $U = \frac{1}{2}$ $Q V = \frac{1}{2}$ $C_{0} V_{0} V \Rightarrow U \infty V$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE