Potentiometer wire of length $1 \,m$ is connected in series with $490\,\Omega $ resistance and $2\,V$ battery. If $0.2\, mV/cm $ is the potential gradient, then resistance of the potentiometer wire is ................ $\Omega$
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A meta sample carrying a current along $x-$ axis with density $J$ is subjected to a magnetic field $B$ (along $z-$ axis). The electric field $E$ developed along $y-$ axis is directly proportional to $J$ as well as $B$. The constant of proportionality has $SI\ unit$
In the circuit shown in figure, the $5\,\Omega $ resistance develops $20.00\,cal/s$ due to the current flowing through it. The heat developed in $2\,\Omega $ resistance (in $cal/s$ ) is
Match the List $I$ with the List $II$ from the combination shown. In the left side (List $I$) there are four different conditions and in the right side (List $II$), there are ratios of heat produced in each resistance for each condition :
List $I$
List $II$
$(I)$ Two wires of same resistance are connected in series and same current is passed through them
$(A)$ $1:2$
$(II)$ Two wires of resistance $R$ and $2R$ $ohm$ are connected in series and same $P . D .$ is applied across them
$(B)$ $4:1$
$(III)$ Two wires of same resistance are connected in parallel and same current is flowing through them
$(C)$ $1:1$
$(IV)$ Two wires of resistances in the ratio $1: 2$ are connected in parallel and same $P . D .$ is applied across the
Figure shows a thick shell made of electrical conductivity $\sigma$ and has inner & outer radii of $10\ cm$ & $20\ cm$ respectively and is filled with ice inside it. Its inside and outside surface are kept at different potentials by a battery of internal resistance $\frac{2}{\pi} \Omega \ \&\ \epsilon = 5V$. Find value of $\sigma$ for which ice melts at maximum possible rate if $25\%$ of heat generated by shell due to joule heating is used to melt ice.
A student uses the resistance of a known resistor $(1 \,\Omega)$ to calibrate a voltmeter and an ammeter using the circuits shown below. The student measures the ratio of the voltage to current to be $1 \times 10^3 \,\Omega$ in circuit $(a)$ and $0.999 \,\Omega$ in circuit $(b)$. From these measurements, the resistance (in $\Omega$ ) of the voltmeter and ammeter are found to be close to
Calculate the amount of charge flowing in $2$ minutes in a wire of resistance $10$ $\Omega$ when a potential difference of $20\,V$ is applied between its ends ............ $C$
Suppose a current carrying wire has a cross-sectional area that, gradually become smaller along the wire, has the shape of a very long cone as shown in figure. Choose the correct statement