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Suppose the drift velocity $v_d$ in a material varied with the applied electric field $E$ as ${v_d}\, \propto \,\sqrt E $ .Then $V - I$ graph for a wire made of such a material is best given by
$10$ resistors each of resistance $10\,\Omega$ can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be $..........$.
Two cells when connected in series are balanced on $8\;m$ on a potentiometer. If the cells are connected with polarities of one of the cell is reversed, they balance on $2\,m$. The ratio of $e.m.f.$'s of the two cells is
A heater is designed to operate with a power of $1000 \mathrm{~W}$ in a $100 \mathrm{~V}$ line. It is connected in combination with a resistance of $10 \Omega$ and a resistance $R$, to a $100 \mathrm{~V}$ mains as shown in figure. For the heater to operate at $62.5 \mathrm{~W}$, the value of $\mathrm{R}$ should be .................. $\Omega$.
In a metre-bridge when a resistance in the left gap is $2\ \Omega$ and unknown resistance in the right gap, the balance length is found to be $40\ \mathrm{~cm}$. On shunting the unknown resistance with $2\ \Omega$, the balance length changes by :
To get maximum current through a resistance of $2.5\,\Omega $, one can use $m$ rows of cells, each row having $n$ cells. The internal resistance of each cell is $0.5\,\Omega $. What are the values of $n$ and $m$ if the total number of cells is $45$ ?
A torch bulb rated as $4.5\, W, 1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ............. $V$
The current $i_1$ and $i_2$ through the resistor $R_1 (= 10\,\Omega )$ and $R_2 (=30 \,\Omega )$ in the circuit diagram with $E_1 = 3\,V, E_2 = 3\,V$ and $E_3 = 2\,V$ are respectively: