A uniform wire of diameter \(d\) carries a current of \(100~\text{mA}\) when the mean drift velocity of electrons in the wire is \(v.\) For a wire of diameter \({\dfrac{d}{2}}\) of the same material to carry a current of \(200~\text{mA},\) the mean drift velocity of electrons in the wire is:
1. \(4v\) 2. \(8v\)
3. \(v\) 4. \(2v\)
Subtopic:  Current & Current Density |
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A uniform metal wire of length \(l\) has \(10~\Omega \) resistance. Now this wire is stretched to a length \(2l\)  and then bent to form a perfect circle. The equivalent resistance across any arbitrary diameter of that circle is:
1. \(10~\Omega \) 2. \(5~\Omega \)
3. \(40~\Omega \) 4. \(20~\Omega \)
Subtopic:  Current & Current Density |
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A copper wire of radius \(1\) mm contains \(10^{22}\) free electrons per cubic metre. The drift velocity for free electrons when \(10\) A current flows through the wire will be:
(Given, charge on electron = \(1.6\times10^{-19}\) C)
1. \(\dfrac{6.25\times10^4}{\pi}\) m/s
2. \(\dfrac{6.25}{\pi}\times10^3\) m/s
3. \(\dfrac{6.25}{\pi}\) m/s
4. \(\dfrac{6.25\times10^5}{\pi}\) m/s
Subtopic:  Current & Current Density |
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A copper wire of length \(10\) m and radius \(\left({10^{-2}/\sqrt{\pi}}\right)\) m has an electrical resistance of \(10~\Omega.\) The current density in the wire for an electric field strength of \(10\) (V/m) is: 
1. \(10^{5}\) A/m2
2. \(10^{4}\) A/m2
3. \(10^{6}\) A/m2
4. \(10^{-5}\) A/m2
Subtopic:  Current & Current Density |
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Match Column I and Column II with appropriate relations.

Column I Column II
(A) Drift Velocity (P) \(\dfrac{ \mathrm{m}}{\mathrm{ne}^2 \rho}\)
(B) Electrical Resistivity (Q) \(nev_d\)
(C) Relaxation Period (R) \(\dfrac{ \mathrm{eE}}{\mathrm{m}} \tau\)
(D) Current Density (S) \(\dfrac{E}{J}\)
 
(A) (B) (C) (D)
1. (R) (P) (S) (Q)
2. (R) (Q) (S) (P)
3. (R) (S) (P) (Q)
4. (R) (S) (Q) (P)
Subtopic:  Current & Current Density |
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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. \(2.25\times 10^{15}~\text{m}^2\text{V}^{-1}\text{s}^{-1}\)

Subtopic:  Current & Current Density |
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