A parallel plate condenser with a dielectric constant K between the plates has a capacity C and is charged to a potential V volt. The dielectric slab between the plates is slowly removed and then reinserted. The net work done by the system in this process is

Question

A parallel plate condenser with a dielectric constant K between the plates has a capacity C and is charged to a potential V volt. The dielectric slab between the plates is slowly removed and then reinserted. The net work done by the system in this process is (A) Zero (B) (1/2)( K -1) CV 2 (C) ( CV 2( K -1)/ K ) (D) (K-1) C V2

Tardigrade Admin · Accepted Answer

Q is constant Case-I

C'=k C Q= same U 1=( Q 2/2 C ')=( Q 2/2 kC ) Case-II

C ''= C Q = same U 2=( Q 2/2 C ) Case-III

C '''= kC Q = same U 3=( Q 2/2 k C ) Work done = U 3- u 1 =0

Q. A parallel plate condenser with a dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V$ volt. The dielectric slab between the plates is slowly removed and then reinserted. The net work done by the system in this process is

Zero

$\frac{1}{2} (K - 1) C V^{2}$

$\frac{C V ^{2} ( K - 1 )}{K}$

$(K - 1) C V^{2}$

Q is constant
Case-I

$C^{'} = k C$
$Q =$ same
$U_{1} = \frac{Q ^{2}}{2 C ^{'}} = \frac{Q ^{2}}{2 k C}$
Case-II

$C^{''} = C$
$Q =$ same
$U_{2} = \frac{Q ^{2}}{2 C}$
Case-III

$C^{'''} = k C$
$Q =$ same
$U_{3} = \frac{Q ^{2}}{2 k C}$
Work done $= U_{3} - u_{1} = 0$

Q. A parallel plate condenser with a dielectric constant K between the plates has a capacity C and is charged to a potential V volt. The dielectric slab between the plates is slowly removed and then reinserted. The net work done by the system in this process is

Zero

21​(K−1)CV2

KCV2(K−1)​

(K−1)CV2

Q is constant Case-I C′=kC Q= same U1​=2C′Q2​=2kCQ2​ Case-II C′′=C Q= same U2​=2CQ2​ Case-III C′′′=kC Q= same U3​=2kCQ2​ Work done =U3​−u1​=0

Q. A parallel plate condenser with a dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V$ volt. The dielectric slab between the plates is slowly removed and then reinserted. The net work done by the system in this process is

$\frac{1}{2} (K - 1) C V^{2}$

$\frac{C V ^{2} ( K - 1 )}{K}$

$(K - 1) C V^{2}$

Q is constant
Case-I

$C^{'} = k C$
$Q =$ same
$U_{1} = \frac{Q ^{2}}{2 C ^{'}} = \frac{Q ^{2}}{2 k C}$
Case-II

$C^{''} = C$
$Q =$ same
$U_{2} = \frac{Q ^{2}}{2 C}$
Case-III

$C^{'''} = k C$
$Q =$ same
$U_{3} = \frac{Q ^{2}}{2 k C}$
Work done $= U_{3} - u_{1} = 0$