Two wires of resistance $R_1$ and $R_2$ have temperature coefficient of resistance ${\alpha _1\,}{\rm{ and \,}}{\alpha _2}$, respectively. These are joined in series. The effective temperature coefficient of resistance is
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$A$ battery of $\mathrm{emf}$ $E_0 = 12\, V$ is connected across a $4\,m$ long uniform wire having resistance $4\,\Omega /m$. The cells of small $\mathrm{emfs}$ $\varepsilon_1 = 2\,V$ and $\varepsilon_2 = 4\,V$ having internal resistance $2\Omega$ and $6\Omega$ respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point $N$, the distance of point $N$ from the point $A$ is equal to
A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery, used across the potentiometer wire, has an emf of $2.0\,V$ and a negligible internal resistance. The potentiometer wire itself is $4\,m$ long. When the resistance $R,$ connected across the given cell, has values of $(i)$ infinity $(ii)$ $9.5\,\Omega$ the balancing lengths on the potentiometer wire are found to be $3\,m$ and $2.85\,m,$ respectively. The value of internal resistance of the cell is ............... $\Omega$
If $n,\,e,\,\tau $ and $m$ respectively represent the density, charge relaxation time and mass of the electron, then the resistance of a wire of length $l$ and area of cross-section $A$ will be
Two cells are connected in opposition as shown. Cell $\mathrm{E}_1$ is of $8 \mathrm{~V}$ emf and $2 \ \Omega$ internal resistance; the cell $E_2$ is of $2 \mathrm{~V}$ emf and $4\ \Omega$ internal resistance. The terminal potential difference of cell $\mathrm{E}_2$ is:
$10$ wires (same length, same area, same material) are connected in parallel and each has $1$ $\Omega$ resistance, then the equivalent resistance will be .............. $\Omega$
A current $I$ flows through a uniform wire of diameter $d,$ when the mean drift velocity is $v_d.$ The same current will flow through a wire of diameter $d/2$ made of the same material, if the mean drift velocity of the electrons is