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Two bulbs consume same power when operated at $200\, V$ and $300\, V$ respectively. When these bulbs are connected in series across a $D.C$. source of $500\, V$, then
A wire of circular cross section has inner portion of radius $R$ made of material of resisitivity $\rho$ and is surrounded by an outer portion of thickness $R$ made of a material of double resisitivity. Find the resistance of length $l$ of such wire
In the given circuit of potentiometer, the potential difference $E$ across $AB$ ( $10\, m$ length) is larger than $E _{1}$ and $E _{2}$ as well. For key $K _{1}$ (closed), the jockey is adjusted to touch the wire at point $J_{1}$ so that there is no deflection in the galvanometer. Now the first battery $\left( E _{1}\right)$ is replaced by second battery $\left( E _{2}\right)$ for working by making $K _{1}$ open and $K _{2}$ closed. The galvanometer gives then null deflection at $J _{2}$. The value of $\frac{ E _{1}}{ E _{2}}$ is $\frac{ a }{ b },$ where $a =$ ...............
Three resistors of $4\,\Omega ,6\,\Omega $ and $12\,\Omega $ are connected in parallel and the combination is connected in series with a $1.5\, V$ battery of $1\,\Omega $ internal resistance. The rate of Joule heating in the $4\,\Omega $ resistor is ................ $W$
Four resistances of $100$ $\Omega$ each are connected in the form of square. Then, the effective resistance along the diagonal points is .............. $\Omega$