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Two wires '$A$' and '$B$' of the same material have their lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. The two wires are connected in parallel across a battery. The ratio of the heat produced in '$A$' to the heat produced in '$B$' for the same time is
Water boils in an electric kettle in $20$ minutes after being switched on. Using the same main supply, the length of the heating element should be. . . . . . .to . . . . . .. times of its initial length if the water is to be boiled in $15$ minutes.
A potentiometer wire has length $10\, m$ and resistance $20\,\Omega $. A $2. 5\, V$ battery of negligible internal resistance is connected across the wire with an $80\,\Omega $ series resistance. The potential gradient on the wire will be
A battery of $e.m.f.$ $10\, V$ and internal resistance $0.5\, ohm$ is connected across a variable resistance $R$. The value of $R$ for which the power delivered in it is maximum is given by ......... $ohm$
Two wires $A$ and $B$ of the same material, having radii in the ratio $1: 2$ carry currents in the ratio $4: 1$. The ratio of drift speed of electrons in $A$ and $B$ is
Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown resistor $R$ is ............. $\Omega$