In the circuit shown the variable resistance is so adjusted that the ammeter reading is same in both the position $1$ and $2$ of the key. The reading of ammeter is $2A$. If $E = 20V$, then $x$ is :- ................... $\Omega$
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What equal length of an iron wire and a copper-nickel alloy wire, each of $2 \; {mm}$ diameter connected parallel to give an equivalent resistance of $3 \Omega ?$
(Given resistivities of iron and copper-nickel alloy wire are $12 \;\mu \Omega {cm}$ and $51\; \mu \Omega {cm}$ respectively) (in ${m}$)
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 arrangement shown in figure when the switch $S_2$ is open, the galvanometer shows no deflection for $l = L/2$. When the switch $S_2$ is closed, the galvanometer shows no deflection for $l = 5L /12$ . The internal resistance $(r)$ of $6\, V$ cell, and the $\mathrm{emf}$ $E$ of the other battery are respectively