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In the given circuit the internal resistance of the $18\,V$ cell is negligible. If $R_1 = 400 \,\Omega ,\,R_3 = 100\,\Omega $ and $R_4 = 500\,\Omega $ and the reading of an ideal voltmeter across $R_4$ is $5\,V,$ then the value of $R_2$ will be ........... $\Omega$
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 '$D$'.
For current entering at $A$, the electric field at a distance '$r$'
from $A$ is
$A, \,B$ and $C$ are voltmeters of resistance $R, \,1 .5R$ and $3R$ respectively as shown in the figure. When some potential difference is applied between $X$ and $Y,$ the voltmeter readings are $V_A, \,V_B$ and $V_C$ respectively. Then
In the electric network shown, when no current flows through the $4\, \Omega $ resistor in the arm $EB$, the potential difference between the points $A$ and $D$ will be ............... $V$
Each element in the finite chain of resistors shown in the figure is $\,1\,\Omega $ . A current of $1\, A$ flows through the final element. Then what is the potential difference $V$ across input terminals of the chain .................. $\mathrm{volt}$