R

2:1

Parallel (i.e)R

Increasing in heat

Reduced by half

When a current I draws from a cell of emf E and internal resistance r, then the terminal voltage
V = E - lr

According to the colour code of resistances. Code for red = 2, Code for green = 5 and Code for yellow = 4
∴ Resistance of the wire = 25 x 10⁴Ω ± 20%

In silicon, the resistivity increases with decrease in temperature.
In copper, the resistivity decreases with decrease in temperature.

Resistance of a conductor of length I and radius r is given by
\(\mathrm{R}=\rho \frac{1}{\pi r^2}\)

Relation between current and drift velocity of electrons in a conductor is given by
I = Anev_d
where, I = current,
A = area of conductor,
n = number density of electrons and
v_d = drift velocity.
with the increase in temperature of a metallic conductor, resistance increases and hence, drift velocity decreases.

The electrical conductivity (σ) of a metallic wire is defined as the ratio of the current density to the electric field it creates. Its SI unit is mho per meter (Ω^-1/m)

Variation of current versus voltage for the material GaAs.

The resistance of the whole wire is 8Ω, which is bent in the form of a circle. We have to find the effective resistance between the ends of diameter AB. Diameter of the circle divides the circle into two equal parts. The resistance of each such part will be 8/2 = 4Ω
(Resistance R ∝ length of wire l, if length is halved then resistance will also become half). From the figure, it is clear that both the parts are in parallel combination. So, effective resistance between A and B is given by
\( \frac{1}{R_{A B}}=\frac{1}{R_1}+\frac{1}{R_2} \\ \Rightarrow \frac{1}{R_{A B}}=\frac{1}{4}+\frac{1}{4} \)


\( \Rightarrow R_{A B}=\frac{a}{1+1}=2 \Omega \\ \mathrm{R}_{\text {effective }}=2 \mathrm{R} \)

In adsorption there is a decrease in residual forces of the surface which evolves as heat. Hence it is exothermic in nature.

When a constant current flows through a wire, the potential difference, between any two points on the wire of uniform cross section, is directly proportional to the length of the wire between these points,
Alternatively:
\(V a l or / dl= \)constant

Nichrome wire having more resistivity (p) will heat up more, as heat produced \(=I^2 R=I^2 \rho \frac{l}{A}\)

When an electron approaches a junction, in addition to the uniform electric field E facing it normally, it keeps the drift velocity fixed. as drift velocity depends on E by the relation of drift velocity,  \(v_d = \frac{eEr}{m}.\) This results into accumulation of changes on the surface of wires at the junction. These produce an additional electric field. These fields change the direction conserving momentum. Thus, the motion of a charge junction is not momentum conserving.

Nichrome

Electric field intensity E = V/l = a constant.

If it is not so, then the balance point will not be obtained on the potentiometer wire.

Slide wire bridge and post office box.

When a cell is short-circuited, it gets totally discharged. The potential difference between the two plates of the cell becomes zero.

In a parallel combination of resistors, the effective area of a cross-section of the conductor increases. As ​\(R∝l,\)​ therefore, resistance decreases.

Ler R is the resistance of the conductor. In the first case, current in a conductor, I = V/R.
In second case current in conductor,
\(I^{\prime}=\frac{2 V+V}{R}=\frac{3 V}{R}=3 I\)
\(As I=n Aev _d or v_d \propto I(\because n, A , are constant) \)
\(\therefore \frac{v_d^{\prime}}{v_d}=\frac{I^{\prime}}{I}=\frac{3 I}{I}=3 \text { or } v_d^{\prime}=3 v_d\)
It means drift velocity becomes tripled.

Yes, the formula defines resistance R = V/I and not Ohm's law, for which, \(\frac{V}{I}=R=\text { constant } \)

The best conductor is silver because electrical conductivity is inversely proportional to the resistivity and resistivity of silver is least.

Drift velocity is the average velocity with which the free electrons get drifted towards the positive end of the conductor under the influence of an external electric field applied.
The relation between current I and drift velocity  v_d is I = nAev_d
Where n is the number density of electrons in a conductor of area of cross-section A and e is the charge on an electron. 

Yes. A steady current in a cylindrical conductor if electric force is acting on free electrons which make the electrons to move in a particular direction. It is possible due to electric field within the conductor.

Electric current is a scalar quantity because it does not follow the laws of vectors addition, i.e., the angle between the wires carrying the current does not affect the total current in the circuit.