A copper wire has a square cross-section, $2.0\, mm$ on a side. It carries a current of $8\, A$ and the density of free electrons is $8 \times {10^{28}}\,{m^{ - 3}}$. The drift speed of electrons is equal to
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Two wires that are made up of two different materials whose specific resistance are in the ratio $2 : 3$, length $3 : 4$ and area $4 : 5$. The ratio of their resistances is
Three unequal resistors in parallel are equivalent to a resistance $1\, ohm$. If two of them are in the ratio $1 : 2$ and if no resistance value is fractional, the largest of the three resistances in $ohms$ is
A cell of $emf\;4\,V$ and internal resistance $0.5\,\Omega$ is connected to a $7.5\,\Omega$ external resistance. The terminal potential difference of the cell is $.....\,V$.
Two students $P$ and $Q$ perform an experiment to verify Ohm's law for a conductor with resistance $R$. They use a current source and a voltmeter with least counts of $0.1 mA$ and $0.1 \,mV$, respectively. The plots of the variation of voltage drop $V$ across $R$ with current $I$ for both are shown below. The statement which is most likely to be correct?
When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor $\mathrm{R}$, the rate of heat produced in $R$ is $J_1$. When the same batteries are connected in parallel across $R$, the rate is $\mathrm{J}_2$. If $\mathrm{J}_1=2.25 \mathrm{~J}_2$ then the value of $\mathrm{R}$ in $\Omega$ is
In the circuit shown, the power developed in the $6\,\Omega $ resistor is $6\,W.$ The power developed in the $4\,\Omega $ resistor is .............. $W$
A wire of resistor $R$ is bent into a circular ring of radius $r$. Equivalent resistance between two points $X$ and $Y$ on its circumference, when angle $XOY$ is $\alpha$, can be given by
A potentiometer consists of two wires $AC$ and $CB$ of same material and of equal lengths but diameters in the ratio $3 : 1.$ Then the potential gradients on the two wires will be in the ratio :-