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
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Two resistors $400\, \Omega$ and $800\, \Omega$ are connected in series across a $6 V$ battery. The potential difference measured by a voltmeter of $10\, k \Omega$ across $400\, \Omega$ resistor is close to$....V$
In the circuit shown, $n$-identical resistors $R$ are connected in parallel $(n > 1)$ and the combination is connected in series to another resistor $R_0$. In the adjoining circuit $n$ resistors of resistance $R$ are all connected in series alongwith $R_0$. The batteries in both circuits are identical and net power dissipated in the $n$ resistors in both circuits is same. The ratio $R_0 / R$ is
In the potentiometer circuit as shown in the figure, the balance length $Al = 60\ cm$ when switch $S$ is open. When switch $S$ is closed and the value of $R$ is $5W$ the balance length $Al' = 50 cm.$ The internal resistance of the cell $C'$ is : .............. $\Omega$
Two square metal plates $A$ and $B$ are of the same thickness and material. The side of $B$ is twice that of $A$. These are connected as shown in series. If the resistances of $A$ and $B$ are denoted by $R_A$ and $R_B,$ then $(R_A/R_B)$ is
The resistance of a bulb filmanet is $100\,\Omega$ at a temperature of $100\,^o C$. If its temperature coefficient of resistance be $0.005$ per $^o C$, its resistance will become $200\,\Omega$ at a temperature of ................ $^oC$
In the experimental setup of meter bridge shown in the figure, the null point is obtained at a distance of $40\,cm$ from $A$. If a $10\,\Omega $ resistor is connected in series with $R_1$, the null point shifts by $10\,cm$. The resistance that should be connected in parallel with $\left( {{R_1} + 10} \right)\,\Omega $ such that the null point shifts back to its initial position is .............. $\Omega$
A potentiometer wire of length $1\,m$ and resistance $10\,\Omega$ is connected in series with a cell of $emf$ $2\,V$ with internal resistance $1 \,\Omega$ and a resistance box including a resistance $R$. If potential difference between the ends of the wire is $1\, mV$, the value of $R$ is ............. $\Omega $