Physics Test - 12

KEY CONCEPTS

Bulk Modulus of Elasticity
When a solid or fluid (liquid or gas) is subjected to a uniform pressure all over the surface, such that the shape remains the same, then there is a change in volume.

Then the ratio of normal stress to the volumetric strain within the elastic limits is called as Bulk modulus. This is denoted by K.

Types of Modulus of elasticity

There are three modulus of elasticity namely Young’s modulus (Y), Bulk modulus (K) and modulus of rigidity (η) corresponding to three types of the strain.

Net current through 4 ohm resistor is half the current flowing through 5 ohm resistor.

Here the potential applied across the circuit is is the total current flowing in the circuit and 

Also as the resistor of 12Ω are in parallel the voltage across both of them is equal, also the resistances are equal which means 

In the following figure, output of AND gate is made as input of NOT gate so we get NAND gate as resultant 

Resistance R= (ρl/A) = (ρl²/v)

KEY CONCEPTS

Sharpness of LCR circuit

Quality factor (Q-factor) of series resonant circuit

(i)  The characteristic of a series resonant circuit is determined by the quality factor (Q - factor) of the circuit.

(ii)  It defines sharpness of i - v curve at resonance when Q - factor is large, the sharpness of resonance curve is more and vice-versa.

(iii)  Q - factor also defined as follows

A series LCR circuit with L=0.125/π H,C=500/π nF,R=23Ω is connected to a 230 V variable frequency supply.

(a) What is the source frequency for which current amplitude is maximum? Obtain this maximum value.

(b) What is the source frequency for which average power absorbed by the circuit is maximum ? obtain the value of this maximum power.

(c) For what reactance of the circuit, the power transferred to the circuit is half the power of resonance? What is the current amplitude at this reactance?

(d) If ω is the angular frequency at which the power consumed in the circuit is half the power at resonance, write an expression for ω

(e) What is the Q-factor (Quality factor) of the given circuit?

Ans. (a) 2000Hz. 10√2A

As a given pole (N or S) of suspended magnet goes into the coil and comes out of its, current is induced in the coil in two opposite directions. Therefore, galvanometer deflection goes to left and right both. As amplitude of oscillation of magnet goes on decreasing, so does the amplitude of deflection.

KEY CONCEPTS

Lenz's law

This law gives the direction of induced emf/induced current. According to this law, the direction of induced emf or current in a circuit is such as to oppose the cause that produces it. This law is based upon law of conservation of energy.

(1) When N-pole of a bar magnet moves towards the coil, the flux associated with loop increases and an emf is induced in it. Since the circuit of loop is closed, induced current also flows in it.

(2) Cause of this induced current, is approach of north pole and therefore to oppose the cause, i.e., to repel the approaching north pole, the induced current in loop is in such a direction so that the front face of loop behaves as north pole. Therefore induced current as seen by observer O is in anticlockwise direction. (figure)

Ohm's Law

If the physical conditions of the conductor (length, temperature, mechanical strain etc.) remains same, then the current flowing through the conductor is directly proportional to the potential difference across it's two ends.
I ∝ V

V = IR ; where R is a proportionality constant, known as electric resistance.

i. Ohm's law is not a universal law, the substances, which obey ohm's law are known as ohmic substance.

ii. Graph between V and i for a metallic conductor is a straight line as shown. At different temperatures V-i curves are different

Microscopic View of Ohm's Law:

When electric current in a material is proportional to the voltage across it, the material is said to be "ohmic", or to obey Ohm's law. A microscopic view suggests that this proportionality comes from the fact that an applied electric field superimposes a small drift velocity on the free electrons in a metal. For ordinary currents, this drift velocity is on the order of millimeters per second in contrast to the speeds of the electrons themselves which are on the order of a million meters per second. Even the electron speeds are themselves small compared to the speed of transmission of an electrical signal down a wire, which is on the order of the speed of light, 300 million meters per second.

Faraday's laws of electrolysis

Faraday’s law electrolysis

Michael Faraday (1834) stated two laws on the basis of his studies on electrolysis:

i. Faraday’s first law

According to this law, The amount of substance liberated at an electrode is directly proportional to the quantity of electricity passed.

Or M or W∝Q

Where W or M = amount of substance liberated in grams.

Q = quantity of electricity passed in coulomb.

Since Q = I.t

Where I = Current in ampere

And t = time in seconds

Hence W∝I.t or W=Z It=ZQ

Where Z = proportionality constant, called electrochemical equivalent.

If I = 1 ampere and t = 1 second then Z = W Therefore electrochemical equivalent may be defined as, “The mass of substance (in grams) liberated at the electrode on passing current of 1 ampere for 1 second or on passing 1 coulomb of electricity is called electrochemical equivalent of the substance”.

Due to polarization, intensity of unpolarised right reduces to half of its value.

KEY CONCEPTS

Variation in Light Intensity Through a Polaroid

Polaroids : It is a device used to produce the plane polarised light. It is based on the principle of selective absorption and is more effective than the tourmaline crystal. or It is a thin film of ultramicroscopic crystals of quinine idosulphate with their optic axis parallel to each other.

PoIaroids allow the light oscillations parallel to the transmission axis pass through them.

Malus law : This law states that the intensity of the polarised light transmitted through the analyser veries as the square of the cosine of the angle between the plane of transmission of the analyser and the plane of the polariser

Polarisation

The phenomenon of limiting the vibrating of electric field vector in one direction in a plane perpendicular to the direction of propagation of light wave is called polarization of light.

(i) The plane in which oscillation occurs in the polarised light is called plane of oscillation.

(ii) The plane perpendicular to the plane of oscillation is called plane of polarisation.

(iii) Light can be polarised by transmitting through certain crystals such as tourmaline or polaroids.

Emission of photo-electron starts from the surface after incidence of photons in about 10^-10 sec.

KEY CONCEPTS

Rate Of Photon Emission From A Light Source
A light source gives off a discrete number of photons each second, emitting its energy in the form of fixed packets. The amount of energy in each photon depends on the light's wavelength, with Planck's constant describing the relationship between the two. You can therefore calculate the light source's photon emission rate from its wavelength.

Particle nature of light was established by photoelectric effect.

KEY CONCEPTS

Einstein's Theory Of Photoelectric effect

According to classical electromagnetic theory, this effect can be attributed to the transfer of energy from the light to an electron in the metal. From this perspective, an alteration in either the amplitude or wavelength of light would induce changes in the rate of emission of electrons from the metal. Furthermore, according to this theory, a sufficiently dim light would be expected to show a lag time between the initial shining of its light and the subsequent emission of an electron. However, the experimental results did not correlate with either of the two predictions made by this theory.

Instead, as it turns out, electrons are only dislodged by the photoelectric effect if light reaches or exceeds a threshold frequency, below which no electrons can be emitted from the metal regardless of the amplitude and temporal length of exposure of light. To make sense of the fact that light can eject electrons even if its intensity is low, Albert Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets (photons), each with energy hf. This shed light onMax Planck's previous discovery of the Planck relation (E = hf) linking energy (E) and frequency (f) as arising from quantization of energy. The factor h is known as the Planck constant.