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A battery of internal resistance $4\,\Omega $ is connected to the network of the resistance as shown in Fig. If the maximum power can be delivered to the network, the magnitude of $R$ in $\Omega $ should be
A $50\,V$ battery is connected across a $10\, ohm$ resistor. The current is $4.5\, amperes$. The internal resistance of the battery is ............. $ohm$
Two electric bulbs whose resistance are in the ratio of $1: 2$, are connected in parallel to a constant voltage source. The power dissipated in them has the ratio
A potentiometer circuit is set up as shown. The potential gradient, across the potentiometer wire, is $k$ $volt/cm$ and the ammeter, present in the circuit, reads $1.0\,\, A$ when two way key is switched off. The balance points, when the key between the terminals $(i)$ $1$ and $2$ $(ii)$ $1$ and $3,$ is plugged in, are found to be at lengths $l_1$ and $l_2$ respectively. The magnitudes, of the resistors $R$ and $X,$ in $ohms$, are then, equal, respectively, to
A current of $2\,A$ flows through a wire of crosssectional area $25.0\,mm ^2$. The number of free electrons in a cubic meter are $2.0 \times 10^{28}$. The drift velocity of the electrons is $...............\times 10^{-6}\,ms ^{-1}$ (given, charge on electron $=1.6 \times 10^{-19}\,C$ )
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