In the given figure the capacitor of plate area A is charged upto charge q. The ratio of elongations…

Q: In the given figure the capacitor of plate area A is charged upto charge q. The ratio of elongations (neglect force of gravity) in springs C and D at equilibrium position is

Numerical

(a) $ \displaystyle \frac{k_1}{k_2} $

(b) $ \displaystyle \frac{k_2}{k_1} $

(c) $ \displaystyle k_1 k_2 $

(d) $ \displaystyle \sqrt{ \frac{k_1}{k_2}} $

Click to See Answer :
Ans: (b)
Sol: Force acting between plates of capacitor is attractive & it is

$ \displaystyle F = \frac{q^2}{2 \epsilon_0 A} $

$\displaystyle k_1 x_1 = k_2 x_2 $

$\displaystyle \frac{x_1}{x_2} = \frac{k_2}{k_1} $

 

Two identical capacitors are connected as shown in the figure. A dielectric slab is introduced between …

Q: Two identical capacitors are connected as shown in the figure. A dielectric slab is introduced between the plates of one of the capacitors so as to fill the gap, the battery remaining connected. The charge on each capacitor will be (charge on each condenser is q0; k = dielectric constant)

Numerical

(a) $ \displaystyle \frac{2 q_0}{1+\frac{1}{k}}$

(b) $ \displaystyle \frac{ q_0}{1+\frac{1}{k}}$

(c) $ \displaystyle \frac{2 q_0}{1+k}$

(d) $ \displaystyle \frac{ q_0}{1+k}$

Click to See Answer :
Ans: (a)
Sol: $ q_0/C + q_0/C = 2 $ …(i)

After introduction of slab , let charge be q1

$q_1/C + q_1/kC = 2$ …(ii)