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Current $I$ is flowing through the two materials having electrical conductivities $\sigma_1$ and $\sigma_2$ respectively $(\sigma_1 > \sigma_2 )$ as shown in the figure. The total amount of charge at the junction of the materials is
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
The internal resistance of a primary cell is $4\, ohm$. It generates a current of $0.2\, amp$ in an external resistance of $21\, ohm$. The rate at which chemical energy is consumed in providing the current is .............. $J/s$
The heating coils rating at $220\, volt$ and producing $50\, cal/sec$ heat are available with the resistances $55\,\Omega $ , $110\,\Omega$ , $220\,\Omega $ and $440\,\Omega $. The heater of maximum power will be of............. $\Omega$