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1. 1 mm/s.

2. The average time between two successive collision is called relaxation time.

3.  V_d = \(\frac{eE}{m}t\)

4. We know drift velocity

V_d = \(\frac{eE}{m}t\)

When temperature increases, relaxation time decreases. As a result drift velocity decreases.

1. ρ = \(\frac{RA}{l}\)

2. Temperature and Nature of metal 

3. We know current density

J = nv_de

But V_d = \(\frac{eE}{m}\tau\)

∴ \(\bar J=n.\frac{e\overrightarrow E}{m}\tau e\)

\(\bar J=\frac{ne^2}{m}\tau \overrightarrow E\)

\(\bar{J}=\sigma\overrightarrow E\)      where \(\sigma = \frac{ne^2}{m}\tau\)

But ρ = \(\frac{1}{\sigma}=\frac{m}{ne^2\tau}\)

4. When temperature increases, the amplitude of oscillation of atom increases. This will decrease . the relaxation time and hence resistivity increases.

Correct option is: (b) 4 A.

Correct option is (C) 1.0 V

The potential difference between two points is equal to the work done in moving a unit positive charge from one point to the other. It's S.I. unit is Volt.

Current is defined as the rate of flow of charge.

 I = Q/t

 Its S.I. unit is Ampere.

Electric potential at a point is defined as the amount of work done in bringing a unit positive charge from infinity to that point. Its unit is the volt.

Color code for Carbon resistors: 

Carbon resistors consists of a ceramic core, on which a thin layer of crystalline carbon is deposited. These resistors are inexpensive, stable and compact in size. Color rings are used to indicate the value of the resistance according to the rules. 

Three coloured rings are used to indicate the values of a resistor: the first two rings are significant figures of resistances, the third ring indicates the decimal multiplier after them. The fourth color, silver or gold, shows the tolerance of the resistor at 10% or 5%. If there is no fourth ring, the tolerance is 20%. For the resistor, the first digit = 5 (green), the second digit = 6 (blue), decimal multiplier = 10³ (orange) and tolerance = 5% (gold). The value of resistance = 56 x 10³ Q or 56 kΩ with the tolerance value 5%.

Correct answer is (b) 41 x 10² Ω

The value of resistance of a resistor having four colour bands in the order yellow, violet , orange and silver is 47000 ± 10%. 

The bulb will not glow There is no potential difference between P and Q. Hence there is no flow of current and the bulb does not flow.

Potential Difference and Current: There should be a potential difference between two points of a conductor if there is to be flow of current between them. Current flows from a point of high electric potential to a point of low electric potential.

The unit of potential difference is volt (V). Voltameter is the device to measure this. If 1 joule of work is done to move one coulomb charge from one point to another, then the potential difference between the points is 1 volt.

(i) Yes, the flow of electric charge will sustain.

(ii) In the first circuit, there is a flow of charge for a short interval of time. There is a continuous flow of charge in the second.

Principle: The potential drop across a part of the potentiometer wire is directly proportional to the length of that part of the wire of uniform cross section.

V = kl

Where k is potential gradient.

Current sensitivity of potentiometer wire is also known as potential gradient, and it can be increased.

(i) By increasing the total length of the wire, keeping terminal voltage constant.

(ii) By connecting a suitable extra resistance R in series with the potentiometer. So, less amount of the current flows through the potentiometer wire.

Reasons: At the balance point, there is no net current drawn from the cell, and cell is in open circuit condition. Voltmeter has some resistance, when connected across the cell. Some current is drawn, as a result emf of the cell decreases. Hence, emf of the cell cannot be measured by the voltmeter.

Correct option is (C) 3 : 2

The resistances in the arms P and Q are fixed to a desired ratio. The resistance in the arm R is adjusted so that the galvanometer shows no deflection. Now the bridge is balanced. The unknown resistance X = RQ/P, where P and Q are the fixed resistances in the ratio arms and R is the adjustable known resistance.

If L is the length of the wire used to prepare the resistor with resistance X and r is its radius, then the specific resistance (resistivity) of the material of the wire is given by \(\rho = \cfrac{X\pi r^2}{L}\)

Correct option is (B)V_B = V_D

• The electricity in our homes is brought through the main conducting cable either from the electric pole or from underground cables. 
• Usually, there are three wires in the cable. 

(a) Live wire which brings in the current. It has a red or brown insulation. 

(b) Neutral wire through which the current returns. It is blue or black. 

(c) Earth wire is of yellow or green colour. This is connected to a metal plate buried deep underground near the house and is for safety purposes. 

• In India, the voltage difference between the live and neutral wires is about 220 V. 
• Live and neutral wires are connected to the electric meter through a fuse. 
• They are connected through a main switch, to all the conducting wires inside the home so as to provide electricity to every room.
• In each separate circuit, various electrical appliances are connected between the live and neutral wires. 
• The different appliances are connected in parallel and the potential difference across every appliance is the same.

• The amount of light given out by bulbs in parallel combination will be more than that in series combination. 
• In parallel combination the resistance of the overall circuit decreases whereas in series it increases, so the current flowing through the bulbs in parallel circuit is more. 
• Due to this, intensity of light given out by bulbs in parallel combination is more than the bulbs in series combination.

• Fuse wire is used to protect domestic appliances. 
• It is made of a mixture of substances and has a specific melting point. 
• It is connected in series to the electric appliances. If for some reason, the current in the circuit increases excessively, the fuse wire gets heated and melts.
• The circuit gets broken and the flow of current stops, thus protecting the appliance. 
• This wire is fitted in a groove in a body of porcelain-like non-conducting material. For domestic use, fuse wires with upper limits of 1 A, 2 A, 3 A, 4 A, 5 A and 10 A are used.

Correct option is: (b) 220 V

Resistance = 4.3 x 10⁴ Ω = 43 x 10³ Ω. Therefore, the colour of third band of a coded resistance will be related to a number 3, i.e., orange. 

Factors affecting internal resistance of a cell : 

(1) Larger the separation between the electrodes of the cell, more the length of the electrolyte through which current has to flow and consequently a higher value of internal resistance. 

(2) Greater the conductivity of the electrolyte, lesser is the internal resistance of the cell. i.e., Internal resistance depends on the nature of the electrolyte. 

(3) The internal resistance of an electrolyte is inversely proportional to common area of the electrodes dipping in the electrolyte. 

(4) Internal resistance of a cell depends on the nature of the electrolytes. 

Comparison of emf and potential difference : 

1. The difference of potentials between the two terminals of a cell in an open circuit is called the electromotive force (emf) of a cell. The difference in potentials between any two points in a closed circuit is called potential difference. 

2. The emf is independent of external resistance of the circuit, whereas potential difference is proportional to the resistance between any two points. 

(B) a high resistance is connected in series with the galvanometer

A potentiometer works on the principle that when a steady current flows through a wire of uniform cross section and composition, the potential drop across any length of the wire is directly proportional to that length.  

Thick copper strips offer minimum resistance and hence avoid the error due to end resistance which have not been taken in to account in the meter bridge formula. 

Given: 

R₁ =15Ω 

R₂ = 3Ω 

R₃ = 4Ω

Effective resistance in series (R_s) = ?

R_s = R₁ + R₂ + R₃ 

R_s = 15 + 3 + 4 

R_s = 22Ω

The effective resistance in the circuit is 22Ω.

(a) Ohm’s law (It is not a universal law).

Ohms law is not a universal law because metals do not obey this law at high temperature. Moreover, certain materials (diode and transistors, etc.) does not obey ohms law.

Answer is The second one

If one coulomb of charge is passing through any cross section of a conductor in one second, the amount of current flowing through it is called one ampere. 

[Note: 1 ampere = 1 coulomb per second OR 1A = 1 C/s. The coulomb is named in honour of Charles Augustin de Coulomb (1736 – 1806), French physicist. The ampere is named in honour of Andre Ampere (1175 – 1836), French physicist and mathematician.]

1 Ampere is given as 1 C x 1s.

The cylindrical container of electric cell is made up of Zinc.

Conductivity is the  Reciprocal of resistivity.

R = \(\frac{pl}{A},\) \(p=\frac{RA}{l}=\frac{5\times2}{2}=5\Omega m\)

We have, Q(t) = At² + Bt + C

\(\frac{dQ}{dt}=2At+B\)

= 2 x 5 x 4 + 4 (at t = 4s)

I = 44 A.

Answer is Increases.

Alloys have:

(i) Low value of temperature coefficient and the resistance of the alloy does not vary much with rise in temperature.

(ii) High resistivity, so even a smaller length of the material is sufficient to design high standard resistance.

The current law states that the algebraic sum of the currents meeting at any junction in a circuit is Zero.

Here, l = 1m, R₁ = 10, V = 6V, R₂ = 5Ω

Current flowing in potentiometer wire,

\(I=\frac{V}{R_1\,+\,R_2}=\frac{6}{10+5}=\frac{6}{15}=0.4A\)

Potential drop across the potentiometer wire

V′= IR = 0.4 × 10 = 4V

Potential gradient,

\(K=\frac{V'}{l}=\frac{4}{1}=4V/m\)

Emf of the primary cell = KI = 4 x 0.4 = 1.6 V

(i) This is to ensure that the connections do not contributed any extra, unknown, resistances in the circuit.

(ii) This is done to minimize the percentage error in the value of the unknown resistance.

Alternatively, This is done to have a better "balancing out" of the effects of any irregularity or non-uniformity in the metre bridge wire.

(iii) This can help in increasing the sensitivety of the merter bridge circuit.

Manganin / Constantan / Nichrome

This material has a low temperature (any one) of coefficient of resistance/high resistivity.

(a) The resistivity of a copper wire of very low. Also, the connections are thick, so that the area is quite large and hence the resistance of the wire is almost negligible.

(b) It is preffered to obtain the balance point in the middle of the meter bridge wire because it improves the sensitivity of the meter bridge. 

(c) Constant an is used for meter bridge wire because its temperature coefficient of resistance is almost negligible due to which the increase in temperature of the wire due to flow of current.

A thick copper strip offers a negligible resistance, so does not alter the value of resistances used in the meter bridge.

The resistance in each of the three arms of the network is 4 Ω. Hence, to balance the network, the resistance in the fourth arm must also be 4 Ω.

Hence, the resistance (R) to be connected across. i.e., in parallel to, the 12 Ω resistance should be such that their equivalent resistance is 4Ω.

∴ \(\cfrac14\) = \(\cfrac1{12}\) + \(\cfrac1R\)

∴ \(\cfrac1R\) = \(\cfrac14\) - \(\cfrac1{12}\) = \(\cfrac{3-1}{12}\) = \(\cfrac2{12}\) = \(\cfrac16\)

∴ R = 6 Ω

The resistance of filament,

\(R=\frac{V}{I}=\frac{V^2}{P}\)

At constant voltage V, the resistance

\(R\,\infty\,\frac{1}{P}\)

That is the resistance of filament of 100 W bulb is greater than that of 1000 W bulb.

The ratio of resistances

\(=\frac{R_1}{R_2}=\frac{P_2}{P_1}=\frac{1000}{100}=\frac{10}{1}=10:1\)

Relaxation time is bound to depend on velocities of electrons and ions. Applied electric field affects the velocities of electrons by speeds at the order of 1mm/s, an insignificant effect. Change in T, on the other hand, affects velocities at the order of 10² m/s. This can affect τ significantly. 

[ρ = ρ(E,T ) in which E dependence is ignorable for ordinary applied voltages.]

The metal strips have low resistance and need not be counted in the potentiometer length l₁ of the null point. One measures only their lengths along the straight segments (of lengths 1 meter each). This is easily done with the help of centimeter rulings or meter ruler and leads to accurate measurements.

Because, in order to ensure sensitivity of the bridge, all other resistances used should either have low value or very high value. This also requires a galvanometer of very low resistance or very high resistance and introduces error in the results.

The advantage of null point method in a Wheatstone bridge is that the resistance of galvanometer does not affect the balance point and there is no need to determine current in resistances and galvanometer and the internal resistance of a galvanometer. R_unknown can be calculated by applying Kirchhoff ’s rules to the circuit. We would need additional accurate measurement of all the currents in resistances and galvanometer and internal resistance of the galvanometer.