A parallel-plate capacitor has plate area 20cm^2, plate separatio… - Vidyadip

Question

A parallel-plate capacitor has plate area $20cm^2$, plate separation 1.0mm and a dielectric slab of dielectric constant 5.0 filling up the space between the plates. This capacitor is joined to a battery of emf 6.0V through a $100\text{k}\Omega$ resistor. Find the energy of the capacitor $8.9\mu\text{s}$ after the connections are made.

✓

Answer

$\text{A} = 20\text{cm}^2, \text{d} = 1\text{mm, K} = 5, \text{e} = 6\text{V}$$\text{R}=100\times10^3\Omega,\text{t}=8.9\times10^{-5}\text{s}$
$\text{C}=\frac{\text{KE}_0\text{A}}{\text{d}}=\frac{5\times8.85\times10^{-12}\times20\times10^{-4}}{1\times10^{-3}}$
$=\frac{10\times8.85\times10^{-3}\times10^{-12}}{10^{-3}}=88.5\times10^{-12}$
$\text{q}=\text{EC}\Big(1-\text{e}^{\frac{-\text{t}}{\text{RC}}}\Big)$
$=6\times88.5\times10^{-12}\Big(1-\text{e}^{\frac{-89\times10^{-6}}{88.5\times10^{-12}\times10^4}}\Big)=530.97$
Energy $=\frac{1}{2}\times\frac{500.97\times530}{88.5\times10^{-12}}$
$=\frac{530.97\times530.97}{88.5\times2}\times10^{12}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Electric Current in Conductors→Electric Current in Conductors — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A car is speeding up on a horizontal road with an acceleration a. Consider the following situations in the car.

A ball is suspended from the ceiling through a string and is maintaining a constant angle with the vertical. Find this angle.
A block is kept on a smooth incline and does not slip on the incline. Find the angle of the incline with the horizontal.

What is simple pendulum? Show that the motion of the pendulum is S.H.M. and hence deduce an expression for the time period of pendulum. Also define second's pendulum.

Explain two-dimensional motion by giving an example. Explain the displacement, velocity and acceleration of a particle in two-dimensional motion

An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that $\text{T}=\frac{\text{k}}{\text{R}}\sqrt{\frac{\text{r}^3}{\text{g}}},$ where k is a dimensionless constant and g is acceleration due to gravity.

Test if the following equations are dimensionally correct:

$\text{h}=\frac{2\text{S}\cos\theta}{\rho\text{rg}}$
$\text{u}=\sqrt{\frac{\text{P}}{\rho}}$
$\text{V}=\frac{\pi\text{Pr}^4\text{t}}{8\eta l}$
$\text{v}=\frac{1}{2\pi}\sqrt{\frac{\text{mg}l}{\text{I}}}$

where h = height, S = surface tension, $\rho$ = density, P = pressure, V = volume, $\eta$ = coefficient of viscosity, v = frequency and I = moment of inertia.

A box of 1.00m3 is filled with nitrogen at 1.5 atm at 300K. The box has a hole of an area 0.010 mm2. How much time is required for the pressure to reduce by 0.10atm, if the pressure outside is 1atm.

When a body slides down from rest along a smooth inclined plane making an angle of 45° with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the co-efficient of friction between the body and the rough plane.

A circular disc of mass $10kg$ is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be $1.5s$. The radius of the disc is 15cm. Determine the torsional spring constant of the wire. (Torsional spring constant $\alpha$ is defined by the relation $\text{J}=-\alpha\theta,$ where J is the restoring couple and $\theta$ the angle of twist).

Water leaks out from an open tank through a hole of area $2mm^2$ in the bottom. Suppose water is filled up to a height of 80cm and the area of cross-section of the tank is $0.4m^2$. The pressure at the open surface and at the hole are equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank.

Find the initial speed of water coming out of the hole.
Find the speed of water coming out when half of water has leaked out.
Find the volume of water leaked out during a time interval dt after the height remained is h. Thus find the decrease in height dh in terms of h and dt.
From the result of part c find the time required for half of the water to leak out.

A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in Fig. Find heat exchanged by the engine, with the surroundings for each section of the cycle. $(C_v = (3/2) R)$

AB : constant volume
BC : constant pressur CD : adiabati DA : constant pressure