Five identical cells each of internal resistance $1\, \Omega$ and $emf \;5\, {V}$ are connected in series and in parallel with an external resistance $'R'.$ For what value of $'R',$ current in series and parallel combination will remain the same ? (in $\Omega$)
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If the resistance of a conductor is $5\,\Omega\,\,$ at $\,50\,^oC$ and $7\, \Omega\,$ at $\,100\,^oC$ then the mean temperature coefficient of resistance of the material is ............... $^oC$
In a building there are $15$ bulbs of $45\; \mathrm{W}, 15$ bulbs of $100\; \mathrm{W}, 15$ small fans of $10 \;\mathrm{W}$ and $2$ heaters of $1 \;\mathrm{kW}$. The voltage of electric main is $220\; \mathrm{V}$. The minimum fuse capacity (rated value) of the building will be: .......... $A$
Figure shows a thick shell made of electrical conductivity $\sigma$ and has inner & outer radii of $10\ cm$ & $20\ cm$ respectively and is filled with ice inside it. Its inside and outside surface are kept at different potentials by a battery of internal resistance $\frac{2}{\pi} \Omega \ \&\ \in = 5V$. Find value of $\sigma$ for which ice melts at maximum possible rate if $25\%$ of heat generated by shell due to joule heating is used to melt ice.
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 '$D$'.
$A$ wire of cross-section area $A$, length $L_1$, resistivity $\rho_1$ and temperature coefficient of resistivity $\alpha_1$ is connected to a second wire of length $L_2$, resistivity $\rho_2$ , temperature coefficient of resistivity $\alpha_1$ and the same area $A$, so that wire carries same current. Total resistance $R$ is independent of temperature for small temperature change if (Thermal expansion effect is negligible)
A uniform metallic wire has a resistance of $18\,\Omega $ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is .................. $\Omega$