The current in a wire varies with time according to the equation \(I=(4+2t),\) where \(I\) is in ampere and \(t\) is in seconds. The quantity of charge which has passed through a cross-section of the wire during the time \(t=2\) s to \(t=6\) s will be:

A charged particle having drift velocity of \(7.5\times10^{-4}~\text{ms}^{-1}\) in an electric field of \(3\times10^{-10}~\text{Vm}^{-1}\), has mobility of: 
1. \(2.5\times 10^{6}~\text{m}^2\text{V}^{-1}\text{s}^{-1}\)
2. \(2.5\times 10^{-6}~\text{m}^2\text{V}^{-1}\text{s}^{-1}\)
3. \(2.25\times 10^{-15}~\text{m}^2\text{V}^{-1}\text{s}^{-1}\)
4. \(2.25\times 10^{15}~\text{m}^2\text{V}^{-1}\text{s}^{-1}\)

Drift velocity v_d varies with the intensity of electric field as per the relation: 

1. $v_d\propto E$

2. $v_d\propto \frac{1}{E}$

3. v_d = constant

4. $v_d\propto E^2$ 

The resistance of a wire is \(R\) ohm. If it is melted and stretched to \(n\) times its original length, its new resistance will be:
1. \(nR\)
2. \(\frac{R}{n}\)
3. \(n^2R\)
4. \(\frac{R}{n^2}\)

Two solid conductors are made up of the same material and have the same length and the same resistance. One of them has a circular cross-section of area $A_1$ and the other one has a square cross-section of area $A_2$. The ratio $A_1/A_2$ is:

The dependence of resistivity \((\rho)\) on the temperature \((T)\) of a semiconductor is, roughly, represented by:

1.		2.
3.		4.

The equivalent resistance between \(A\) and \(B\) for the mesh shown in the figure is:

A potential divider is used to give outputs of 2 V and 3 V from a 5 V source, as shown in the figure.

Which combination of resistances, from the ones given below, ${\mathrm{R}}_1,$ ${\mathrm{R}}_2,$ $\mathrm{and}$ ${\mathrm{R}}_3$ give the correct voltages?

In the circuit shown in the figure, the effective resistance between A and B is:

1.  2 $\mathrm{\Omega }$

2.  4 $\mathrm{\Omega }$

3.  6 $\mathrm{\Omega }$

4.  8 $\mathrm{\Omega }$

The effective resistance between points P and Q of the electrical circuit shown in the figure is:
            

1. $2Rr/(R+r)$

2. $8R$ $(R+r)/(3R+r)$

3. $2r+4R$

4. $5R/2$ $+$ $2r$