High value of resistivity and low value of temperature coefficient

Resistivity of Copper is less, hence mangain wire is thicker

Superconductors are the materials that lose all its resistance at very low temperature = 0 K
Applications of Super conductor are used
a) In making very strong electromagnets
b) In producing veru high speed computers

a) in parallel, power dissipation \(\alpha\) 1/R 
Therefore 3\(\Omega \) wire will dissipate more power
b) In series, power dissipation \(\alpha\) R
Therefore 9\(\Omega \) wire will dissipate more power

Now, 1/R = 1R₁ + 1R₂
Because 1 = 48/240 = 0.2 m

\(\mathrm{R}=\rho(1 / \mathrm{A})\)
\( =\rho\left(1^2 / \mathrm{A} 1\right) \\ =\rho 12 / \mathrm{V} \)
Since \(\rho\) and V are constans therefore
\(\rightarrow\left(R_2 / R_1\right)=\left(12 / l_1\right)^2=9\)
Because R₂ = 9R₁
\(=9 \times 10=90 \Omega\)

As Vd α V
The different velocity will be doubled

It is so because the filament of the electric bulb has high melting point and it remains safe in an atmosphere of inert gases which protect its oxidation.

This impression is misleading. In fact, there is no special attractive force that keeps a person stuck with a high power line while touching that wire, whereas a current of few milliampere is enough to disorganise our nervous system. As a result of it, the affected person loses temporarily his ability to exercise his nervous control to get himself free from the high power line.

When a person accidently touches the line wire of a 240 V supply, a current I = 240/10000 = 0.024 A = 24 mA, flows through the body of the person. This current interferes with the nerve process related to our heart beating, which is basically electrical in nature, this, in turn, accounts for a strong shock.

Every metal conductor has a large number of free electrons which move at random at room temperature. Their average thermal velocity at any instant is zero. When a pot. diff. is applied across the ends of the conductor, an electric field is set up in the conductor. Due to it, the free electrons of the conductor experience force due to the electric field and drift towards the positive end of the conductor, causing the electric current in the conductor. The direction of conventional current is opposite to the direction of motion of the free electrons in the conductor.

With the increase in temperature, the drift velocity of free electrons in a metal conductor decreases due to increase in collision frequency of free electrons with the atom/ions of the conductor.

A constant current can be kept inside a conductor by maintaining a constant potential difference across the two ends of conductor.

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.

The man is excited due to the transfer of electric energy to his body.

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.

0.02V m^-1 
0.12V

1.5\(\Omega\)

From Kirchhoff's junction rule, we have
\( { I }_{ 1 }={ I }+{ I }_{ 2 }\)   ...........(i)
Applying Kirchhoff's loop rule to outer loop containing 10V cell, we get
\(10=IR+{ 10I }_{ 1 }\) ............(ii)
Applying Kirchhoff's loop rule to outer loop containing 2V cell, we get
\(2={ 5I }_{ 2 }-RI\)
\(2=5\left( { I }_{ 1 }-I \right) -RI\)
\(4={ 10I }_{ 1 }-10I-2RI\)
Subtracting eq (ii) from eq (i), we get
\(6=3RI+10I\)
\(2=I\left( R+\frac { 10 }{ 3 } \right) \)
From Ohm's law, we have
\(V=I\left( R+{ R }_{ off } \right) \)
Comparing eq (iii) and (iv), we get
\({ R }_{ ef }=\frac { 10 }{ 3 } \Omega \)
If \({ E }_{ eff }\) and \({ R }_{ eff }\) are the effective voltage and effective internal resistance of the combination, then the equivalent circuit is shown.

According to the question, the circuit can be drawn as shown in the figure
 
where ε = 2 V, and r = internal resistance of each cell
An equivalent circuit can be redraw as shown.
\( \frac{r}{4} =\left[\frac{E-V}{V}\right] \times R \)
\(=\left[\frac{2-1.6}{1.6}\right] \times 7.5 \)
\(r =7.5 \Omega \)

Conductance,  
G = \(\frac{1}{R}=\frac{1}{0.01}\)= 100 S
conductivity,
\(\sigma =\frac{1}{\rho}=\frac{l}{RA}=\frac{0.1}{0.01 \times 10^{-4}}\)
= 10⁵ S m^-1

The potential, V = constant, l' = 3l
(i) Drift speed of electrons, \(v_d=\frac{V}{n e l \rho}\)
\(v_d \propto \frac{1}{l}\)  [\(\because\) other factors are constant]
So, when length is tripled, drift velocity gets one-third.
(ii) Resistance of conductor is \(R=\rho \frac{l}{A} .\)
Here, wire is tretched to triple its length, that means the mass of the wire remains same in both conditions.
Before stretching mass = After stretching mass
M₁ = M₂
\(\begin{aligned} & \Rightarrow \quad V_1 \rho_1=V_2 \rho_2 \quad\left[\because \rho_1=\rho_2\right] \\ \end{aligned}\)
or \(\begin{aligned} \quad A_1 l_1=A_2 l_2 \end{aligned}\)
Since, length is tripled after stretching.
\(\therefore \quad A_1 l=A_2(3 l) \text { or } A_2=\frac{A_1}{3}\)
Hence, \(R_2=\rho \frac{l_2}{A_2}=\rho \frac{3 l}{A_1 / 3}=\frac{9 \rho l}{A_1} \Rightarrow R_2=9 R_1\)
Thus, new resistance is 9 times of its original value.

(a) Alloys of metals usually have greater resistivity than that of their constituent metals.
(b) Alloys usually have much lower temperature coefficients of resistance than pure metals.
(c) The resistivity of the alloy manganin is nearly independent of increase of temperature.
(d) The resistivity of a typical insulator is greater than that of a metal by a factor of the order of 10²².