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:

1. \(60\) C  2. \(24\) C
3. \(48\) 4. \(30\) C

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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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. \(v_{d}= \text{constant}\)
4. \(v_{d} \propto E^2\)

Subtopic:  Current & Current Density |
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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. \(\frac{R}{n^2}\)
Subtopic:  Derivation of Ohm's Law |
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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 A1 and the other one has a square cross-section of area A2. The ratio A1/A2 is:

1. \(1.5\) 2. \(1\)
3. \(0.8\) 4. \(2\)
Subtopic:  Derivation of Ohm's Law |
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The dependence of resistivity \((\rho)\) on the temperature \((T)\) of a semiconductor is, roughly, represented by:

1. 2.
3. 4.
Subtopic:  Derivation of Ohm's Law |
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The equivalent resistance between \(A\) and \(B\) for the mesh shown in the figure is:

      

1. \(7.2\) \(\Omega\) 2. \(16\) \(\Omega\)
3. \(30\) \(\Omega\) 4. \(4.8\) \(\Omega\)
Subtopic:  Combination of Resistors |
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A potential divider is used to give outputs of \(2~\text{V}\) and \(3~\text{V}\) from a \(5~\text{V}\) source, as shown in the figure.

Which combination of resistances, from the ones given below, \(R_1, R_2, ~\text{and}~R_3\) give the correct voltages?
1. \({R}_1=1~\text{k} \Omega, {R}_2=1 ~\text{k} \Omega, {R}_3=2 ~\text{k} \Omega\)
2. \({R}_1=2 ~\text{k} \Omega, {R}_2=1~\text{k} \Omega, {R}_3=2~\text{k} \Omega\)
3. \({R}_1=1 ~\text{k} \Omega, {R}_2=2~ \text{k} \Omega, {R}_3=2~ \text{k} \Omega\)
4. \({R}_1=3~\text{k} \Omega, {R}_2=2~\text{k} \Omega, {R}_3=2~ \text{k} \Omega\)
Subtopic:  Combination of Resistors |
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In the circuit shown in the figure, the effective resistance between \(A\) and \(B\) is:

                             

1. \(2~\Omega\)
2. \(4~\Omega\)
3. \(6~\Omega\)
4. \(8~\Omega\)

Subtopic:  Combination of Resistors |
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The effective resistance between points \(P\) and \(Q\) of the electrical circuit shown in the figure is:

1. \(\frac{2 R r}{\left(R + r \right)}\) 2. \(\frac{8R\left(R + r\right)}{\left( 3 R + r\right)}\)
3. \(2r+4R\) 4. \(\frac{5R}{2}+2r\)
Subtopic:  Combination of Resistors |
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