A parallel plate capacitor of capacitance 1 µF is charged to a potential difference of 20 V. The distance between plates is 1 µm. The energy density between plates of capacitor is :

Identify the valid statements relevant to the given circuit at the instant when the key is closed. A. There will be no current through resistor $R$. B. There will be maximum current in the connecting wires. C. Potential difference between the capacitor plates A and B is minimum. D. Charge on the capacitor plates is minimum. Choose the correct answer from the options given below:

A parallel plate capacitor was made with two rectangular plates, each with a length of $l=3\mathrm{cm}$ and breath of $\mathrm{b}=1\mathrm{cm}$. The distance between the plates is $3\mu \mathrm{m}$. Out of the following, which are the ways to increase the capacitance by a factor of 10 ? A. $l=30\mathrm{cm},\mathrm{b}=1\mathrm{cm},\mathrm{d}=1\mu \mathrm{m}$ B. $l=3\mathrm{cm},\mathrm{b}=1\mathrm{cm},\mathrm{d}=30\mu \mathrm{m}$ C. $l=6\mathrm{cm},\mathrm{b}=5\mathrm{cm},\mathrm{d}=3\mu \mathrm{m}$ D. $l=1\mathrm{cm},\mathrm{b}=1\mathrm{cm},\mathrm{d}=10\mu \mathrm{m}$ E. $l=5\mathrm{cm},\mathrm{b}=2\mathrm{cm},\mathrm{d}=1\mu \mathrm{m}$ Choose the correct answer from the options given below:

Two capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are ${\mathrm{U}}_1$ and ${\mathrm{U}}_2$, respectively. Which of the given statements is true?

A parallel plate capacitor is filled equally(half) with two dielectrics of dielectric constants ${\epsilon }_1$ and ${\epsilon }_2$, as shown in figures. The distance between the plates is $d$ and area of each plate is $A$. If capacitance in first configuration and second configuration are ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ respectively, then $\frac{C_1}{C_2}$ is: First Configuration Second Configuration

Three parallel plate capacitors $C_1,C_2$ and $C_3$ each of capacitance $5\mu \mathrm{F}$ are connected as shown in figure. The effective capacitance between points $A$ and $B$, when the space between the parallel plates of $C_1$ capacitor is filled with a dielectric medium having dielectric constant of 4, is :

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V , its capacitance is: (in pF )

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities ${\rho }_1$ and ${\rho }_2$, respectively. The frequency of $9^{\text{th }}$ harmonic of closed tube is identical with $4^{\text{th }}$ harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ${\rho }_1:{\rho }_2=1:16$, then the length of the open tube is :

The equation of a transverse wave travelling along a string is $y(x,t)=4.0\sin \left[20\times 10^{-3}x+600t\right]\mathrm{mm}$, where $x$ is in mm and $t$ is in second. The velocity of the wave is :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$ Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $y_1(x,t)=4\sin (kx-\omega t)$ and $y_2(x,t)=2\sin (kx-\omega t+\frac{2\pi }{3})$, are: (Take the angular frequency of initial waves same as $\omega$)

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is $v_1$, and that in the other string having radius of cross section R/2 is $v_2$. Then $\frac{v_2}{v_1}$ =

Two harmonic waves moving in the same direction superimpose to form a wave $x=\mathrm{a}\cos (1.5\mathrm{t})\cos (50.5\mathrm{t})$ where t is in seconds. Find the period with which they beat. (close to nearest integer)

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$-direction in 0.3 sec . The crest P is at $x=0$ at $\mathrm{t}=0\sec$ and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?

The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

Displacement of a wave is expressed as $x(t)=5\cos \left(628t+\frac{\pi }{2}\right)\mathrm{m}$. The wavelength of the wave when its velocity is $300\mathrm{m}/\mathrm{s}$ is : $$(\pi =3.14)$$

In an experiment with a closed organ pipe, it is filled with water by $\left(\frac{1}{5}\right)$ th of its volume. The frequency of the fundamental note will change by

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire’s cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be :

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :