An electric heater and an electric bulb are rated $500\, W, 220\, V$ and $100\, W, 220\, V$ respectively. Both are connected in series to a $220\, V$ $a.c.$ mains. The power consumed by the heater and the bulb respectively is:

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 $b$,filled 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:

In the given circuit diagram,in the steady state,the current through the battery and the charge on the capacitor respectively are:

$A$ $dc$ source of $emf \, E_1 = 100 \, V$ and internal resistance $r = 0.5 \, \Omega$,a storage battery of $emf \, E_2 = 90 \, V$,and an external resistance $R$ are connected as shown in the figure. For what value of $R$ will no current pass through the battery $E_2$ (in $.5$)? ................ $\Omega$

The figure shows a network of resistors and a battery. If $1\,A$ current flows through the branch $CF$,then answer the following questions. The current through:

An electric current is passed through a circuit containing two wires of the same material,connected in parallel. If the lengths and radii of the wires are in the ratio of $4/3$ and $2/3$ respectively,then the ratio of the currents passing through the wires will be: