A wire of length ' $r$ ' and resistance $100 \Omega$ is divided into $10$ equal parts. The first $5$ parts are connected in series while the next $5$ parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:
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A heater coil connected to a supply of a $220\, V$ is dissipating some power ${P_1}.$ The coil is cut into half and the two halves are connected in parallel. The heater now dissipates a power ${P_2}.$ The ratio of power ${P_1}\,\,:\,\,{P_2}$ is
The figure shows a tetrahedron, each side of which has a resistance $r$ If a battery is connected between any two points of the tetrahedron, then identify the correct statement $(s)$.
In the circuit shown in the figure, the switch $S$ is initially open and the capacitor is initially uncharged. $ I_1, I_2$ and $I_3$ represent the current in the resistance $2\,\Omega , 4\,\Omega $ and $8\,\Omega$ respectively.
Infinite number of cells having $emf$ and internal resistance $\left( {E,r} \right)$, $\left( {\frac{E}{n},\frac{r}{n}} \right)$, $\left( {\frac{E}{{{n^2}}},\frac{r}{{{n^2}}}} \right)$, $\left( {\frac{E}{{{n^3}}},\frac{r}{{{n^3}}}} \right)$..... are connected in series in same manner across an external resistance of $\frac{{nr}}{{n + 1}}$ . Current flowing through the external resistor is
A $6.0\,volt$ battery is connected to two light bulbs as shown in figure. Light bulb $1$ has resistance $3\,ohm$ while light bulb $2$ has resistance $6\,ohm.$ Battery has negligible internal resistance. Which bulb will glow brighter?
Two batteries, one of emf $18\,volts\;emf$ and internal resistance $2\,\Omega $ and the other of emf $12\, volt$ and internal resistance $1\,\Omega $, are connected as shown. The voltmeter $V$ will record a reading of .............. $volt$