Two metal wires of identical dimensions are connected in series. If \(\sigma_1~\text{and}~\sigma_2\) are the conductivities of the metal wires respectively, the effective conductivity of the combination is:

1. \(\frac{2\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\) 2. \(\frac{\sigma_1 +\sigma_2}{2\sigma_1\sigma_2}\)
3. \(\frac{\sigma_1 +\sigma_2}{\sigma_1\sigma_2}\) 4. \(\frac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\)

Subtopic:  Derivation of Ohm's Law |
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A wire of resistance \(4~\Omega\) is stretched to twice its original length. The resistance of a stretched wire would be:

1. \(4~\Omega\) 2. \(8~\Omega\)
3. \(16~\Omega\) 4. \(2~\Omega\)
Subtopic:  Derivation of Ohm's Law |
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Two rods are joined end to end, as shown. Both have a cross-sectional area of \(0.01~\text{cm}^2\). Each is \(1~\text{m}\) long. One rod is of copper with a resistivity of \(1.7\times10^{-6}~\Omega\text{-cm}\), the other is of iron with a resistivity of \(10^{-5}\) \(\Omega\text-\text{cm}.\) How much voltage is required to produce a current of \(1\) A in the rods?
        
1. \(0.00145\) V
2. \(0.0145\) V
3. \(1.7\times10^{-6}\) V
4. \(0.117\) V
Subtopic:  Derivation of Ohm's Law |
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