Two hollow metallic spheres of radii 20 cm a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The capacitance of a spherical conductor is given by $C = 4\pi\epsilon_0 R = \frac{R}{k}$,where $k = \frac{1}{4\pi\epsilon_0} = 9 	imes 10^9 \ N

Vedclass · Accepted Answer

$9 	imes 10^6$

Vedclass · Answer

(A) The capacitance of a spherical conductor is given by $C = 4\pi\epsilon_0 R = \frac{R}{k}$,where $k = \frac{1}{4\pi\epsilon_0} = 9 	imes 10^9 \ N \cdot m^2/C^2$.Given: $R_1 = 0.2 \ m$,$R_2 = 0.1 \ m$,$q_1 = 150 	imes 10^{-6} \ C$,$q_2 = 150 	imes 10^{-6} \ C$.When connected by a wire,the total charge $Q = q_1 + q_2 = 300 	imes 10^{-6} \ C$ is shared,and the total capacitance is $C_{eq} = C_1 + C_2 = \frac{R_1 + R_2}{k}$.The common potential $V$ is given by $V = \frac{Q}{C_{eq}} = \frac{q_1 + q_2}{(R_1 + R_2)/k} = \frac{k(q_1 + q_2)}{R_1 + R_2}$.Substituting the values: $V = \frac{9 	imes 10^9 	imes (300 	imes 10^{-6})}{0.2 + 0.1} = \frac{9 	imes 10^9 	imes 300 	imes 10^{-6}}{0.3}$.$V = \frac{2700 	imes 10^3}{0.3} = 9000 	imes 10^3 = 9 	imes 10^6 \ V$.

Two hollow metallic spheres of radii $20 \ cm$ and $10 \ cm$ each carry a charge of $150 \ \mu C$. If they are connected by a conducting wire,the common potential is ...... $V$.

Similar Questions

$A$ $2 \ \mu F$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $S$ is turned to position $2$ is (in $\%$)

Two metallic charged spheres whose radii are $20\,cm$ and $10\,cm$ respectively,have each $150\,\mu C$ positive charge. The common potential after they are connected by a conducting wire is

$A$ capacitor of capacity $C_1$ is charged up to $V$ volt and then connected to an uncharged capacitor of capacity $C_2$. The final potential difference across each will be:

$A$ $20\,\mu F$ capacitor is charged to a potential of $500\,V$ and then connected in parallel to a $10\,\mu F$ capacitor charged to $200\,V$. What is the common potential in $V$?

$A$ $10 \ \mu F$ capacitor is charged to a potential difference of $50 \ V$ and connected in parallel to another uncharged capacitor. The common potential difference becomes $20 \ V$. The capacitance of the second capacitor is ........ $\mu F$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module