A metal wire of resistance \(3~\Omega\) is elongated to make a uniform wire of double its previous length. This new wire is now bent and the ends are joined to make a circle. If two points on this circle make an angle \(60^\circ\) at the centre, the equivalent resistance between these two points will be:
1. \( \frac{5}{2}~ \Omega \)
2. \( \frac{5}{3} ~\Omega \)
3. \( \frac{7}{2}~ \Omega \)
4. \( \frac{12}{5} ~\Omega\)

A current of \(5~\text{A}\) passes through a copper conductor (resistivity= \(1.7 \times 10^{-8}~\Omega\text{m}\)) of radius of cross-section \(5~\text{mm}\). Find the mobility of the charges if their drift velocity is \(1.1 \times 10^{-3}~\text{m/s}\).
1. \( 1.0 ~\text{m}^2/\text{Vs} \)
2. \( 1.8 ~\text{m}^2/\text{Vs} \)
3. \( 1.5 ~\text{m}^2/\text{Vs} \)
4. \( 1.3~\text{m}^2/\text{Vs} \)

In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line.

One may conclude that:
1. \( R(T) =R_0 e^{T^2 / T_0^2} \)
2. \(R(T) =\frac{R_0}{T^2} \)
3. \(R(T) =R_0 e^{-T^2 / T_0^2} \)
4. \(R(T) =R_0 e^{-T_0^2 / T^2}\)

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity \(\rho_C,\rho_T,\rho_M\) and \(\rho_A\) respectively. Then:
1. \( \rho_C>\rho_A>\rho_T \)
2. \(\rho_M>\rho_A>\rho_C \)
3. \(\rho_A>\rho_T>\rho_C \)
4. \(\rho_A>\rho_M>\rho_C\)

A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit:

A wire of \(1~\Omega\) has a length of \(1\) m. It is stretched till its length increases by \(25~\%\). The percentage change in resistance to the nearest integer is:
1. \(56\%\)
2. \(25\%\)
3. \(12.5\%\)
4. \(76\%\)