In the figure shown, after the switch $‘S’$ is turned from position $‘A’$ to position $‘B’$, the energy dissipated in the circuit in terms of capacitance $‘C’$ and total charge $‘Q’$ is
JEE MAIN 2019, Diffcult
Download our app for free and get started
Before switch is shifted:
Energy stored,
$\mathrm{U}_{1}=\frac{1}{2} \mathrm{CE}^{2}$
and charge stored,
$Q=C E$
After switch is shifted:
$V_{M}-V_{N}=\frac{Q}{4 C}=\frac{C E}{4 C}=\frac{E}{4}$
Energy stored, $U_{f}=\frac{1}{2}(4 \mathrm{C})\left(\frac{E}{4}\right)^{2}=\frac{1}{8} \mathrm{CE}^{2}$
Energy dissipated $=U_{i}-U_{f}=\frac{3}{8} C E^{2}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A charged particle $q$ is shot towards another charged particle $Q$ which is fixed, with a speed $v$. It approaches $Q$ upto a closest distance $r$ and then returns. If $q$ were given a speed $2v$, the closest distances of approach would beView Solution
- 2In the circuit shown in figure, four capacitors are connected to a battery. The maximum energy is stored in the capacitor of.....$\mu F$View Solution
- 3A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is $A\;metr{e^2}$ and the separation is $t$ $metre$. The dielectric constants are ${k_1}$ and ${k_2}$ respectively. Its capacitance in farad will beView Solution
- 4If the dielectric constant and dielectric strength be denoted by $k$ and $x$ respectively, then a material suitable for use as a dielectric in a capacitor must haveView Solution
- 5A particle of mass $m$ and charge $q$ is kept at the top of a fixed frictionless sphere. $A$ uniform horizontal electric field $E$ is switched on. The particle looses contact with the sphere, when the line joining the center of the sphere and the particle makes an angle $45^o$ with the vertical. The ratio $\frac{qE}{mg}$ is :-View Solution
- 6The electric potential at a point $(x,\;y)$ in the $x - y$ plane is given by $V = - kxy$. The field intensity at a distance $r$ from the origin varies asView Solution
- 7A parallel plate capacitor is made of two square plates of side $a$, separated by a distance $d\,(d < < a)$. The lower triangular portion is filled with a dielectric of dielectric constant $K$, as shown in the figure. Capacitance of this capacitor isView Solution
- 8Two charged spheres of radii $10\, cm$ and $15\, cm$ are connected by a thin wire. No current will flow, if they haveView Solution
- 9A capacitor $4\,\mu F$ charged to $50\, V$ is connected to another capacitor of $2\,\mu F$ charged to $100 \,V$ with plates of like charges connected together. The total energy before and after connection in multiples of $({10^{ - 2}}\,J)$ isView Solution
- 10Two electric charges $12\,\mu C$ and $ - 6\,\mu C$ are placed $20\, cm$ apart in air. There will be a point $P$ on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of $P$ from $ - 6\,\mu C$ charge is.......$m$View Solution