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Consider a block of conducting material ofresistivity '$\rho$' shown in the figure. Current '$I$' enters at '$A$' and leaves from '$D$'. We apply superp osition principle to find voltage '$\Delta V$ ' developed between '$B$' and '$C$'. The calculation is done in the following steps:
$(i)$ Take current '$I$' entering from '$A$' and assume it to spread over a hemispherical surface in the block.
$(ii)$ Calculatefield $E(r)$ at distance '$r$' from $A$ by using Ohm's law $E = \rho j$, where j is the current per unit area at '$r$'.
(iii) From the '$r$' dependence of $E(r)$, obtain the potential $V(r)$ at $r$.
(iv) Repeat $(i), (ii)$ and $(iii)$ for current '$I$' leaving '$D$' and superpose results for '$A$' and '$D$'.
The resistance of a wire is $5\,ohm$ at $50\,^o C$ and $6\,ohm $ at $100\,^o C$. The resistance of the wire at $0\,^o C$ will be .............. $\Omega$
In an electrical cable there is a single wire of radius $9\, mm$ of copper. Its resistance is $5\,\Omega $. The cable is replaced by $6$ different insulated copper wires, the radius of each wire is $3\,mm$. Now the total resistance of the cable will be ............... $\Omega$
When $5\ V$ potential difference is applied across a wire of length $0.1\ m$, the drift speed of electrons is $2.5 \times 10^{-4}$ $ms^{-1}$ . If the electron density in the wire is $8 \times 10^{28}$ $m^{-3}$ the resistivity of the material is close to
A cylindrical wire of radius $0.5 \,mm$ and conductivity $5 \times 10^{7}\, S / m$ is subjected to an electric field of $10 \,mV / m .$ The expected value of current in the wire will be $x ^{3} \,\pi mA$. The value of $x$ is ......
A voltmeter having a resistance of $998\, ohms$ is connected to a cell of $e.m.f.$ $2\, volt$ and internal resistance $2\, ohm$. The error in the measurement of $e.m.f.$ will be
An electron (charge $= 1.6 × 10^{-19}$ coulomb) is moving in a circle of radius $5.1 × 10^{-11}\,m$ at a frequency of $6.8 × 10^{15} $ revolutions/sec. The equivalent current is approximately
A battery of $e.m.f.$ $3\, volt$ and internal resistance $1.0\, ohm$ is connected in series with copper voltameter. The current flowing in the circuit is $1.5\, amperes$. The resistance of voltameter will be ........... $ohm$