An electric bulb rated as $200\, {W}$ at $100 \,{V}$ is used in a circuit having $200\, {V}$ supply. The resistance $'R'$ that must be put in series with the bulb so that the bulb delivers the same power is $.....\,\Omega$

A railway compartment is lit up by thirteen lamps each taking $2.1\, amp$ at $15\, volts$. The heat generated per second in each lamp will be ............ $cal$

Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius $'a'$ and a concentric thin cylindrical shell of radius ' $b$ ' fille in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R ,$ the maximum Joule heating in $R$ will take place for

Two electric bulbs rated ${P_1}\,watt$  $V\, volts$ and ${P_2}\, watt$ $V\, volts$ are connected in parallel and $V\, volts$ are applied to it. The total power will be

If $X, Y$ and $Z$ in figure are identical lamps, which of the following changes to the brightnesses of the lamps occur when switch $S$ is closed?

Two identical batteries, each of $e.m.f.$ $2\, volt$ and internal resistance $1.0\, ohm$ are available to produce heat in an external resistance $R = 0.5\,ohm$ by passing a current through it. The maximum Joulean power that can be developed across $R$ using these batteries is ............. $watt$