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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
Two cells of $e.m.f.$ $E_1$ and $E_2$ are joined in series and the balancing length of the potentiometer wire is $625$ $cm$. If the terminals of $E_1$ are reversed, the balancing length obtained is $125 \,cm$. Given $E_2 > E_1$, the ratio $E_1: E_2$ will be
In a conductor, if the number of conduction electrons per unit volume is $8.5 \times 10^{28}\, m^{-3}$ and mean free time is $25\,fs$ (femto second), its approximate resistivity is $\left( {{m_e} = 9.1 \times {{10}^{ - 31}}\,kg} \right)$
A current of $3\,amp$ flows through the $2\,\Omega $ resistor shown in the circuit. The power dissipated in the $5\,\Omega $ resistor is ................. $watt$
An electrical power line, having a total resistance of $2 \Omega$, delivers $1 \,kW$ at $220\, V$. The efficiency of the transmission line is approximately $.......\%$
In the circuit shown in figure potential difference between points A and $B$ is $16\,V$. the current passing through $2 \Omega$ resistance will be $...........\,A$
A rod of length $l$ with thermally insulated lateral surface is made of a material whose thermal conductivity $K$ varies as $K = C/T$ , where $C$ is a constant. The ends are at temperatures $T_1$ and $T_2$ . The heat current density is