The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as $R_1$ has the colour code (Orange, Red, Brown). The resistors $R_2$ and $R_4$ are $80\, \Omega $ and $40\,\Omega $, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as $R_3$ would be
$\therefore $ Colour code of $\mathrm{R}_{3}$ be Brown, Blue, Brown.
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A wire has a non-uniform cross-section as shown in figure.A steady current flows through it. The drift speed of electrons at points $P$ and $q$ is $v_P$ and $v_Q$.
Current density in a cylindrical wire of radius $R$ is given as $J =$ $\left\{ {\begin{array}{*{20}{c}}
{{J_0}\left( {\frac{x}{R} - 1} \right)\,\,for\,\,0 \leqslant x < \frac{R}{2}} \\
{{J_0}\frac{x}{R}\,\,\,\,for\,\,\,\frac{R}{2} \leqslant x \leqslant R}
\end{array}} \right.$The current flowing in the wire is:
Equal potentials are applied on an iron and copper wire of same length. In order to have the same current flow in the two wires, the ratio $r$ (iron)/$r$ (copper) of their radii must be (Given that specific resistance of iron = $1.0 \times {10^{ - 7}}$ $ ohm-m$ and specific resistance of copper = $1.7 \times {10^{ - 8}}\,ohm-m$)
A torch battery consisting of two cells of $1.45\, volts$ and an internal resistance $0.15\,\Omega $, each cell sending currents through the filament of the lamps having resistance $1.5\,ohms$. The value of current will be ....... $A$
Water of volume $2\, litre$ in a container is heated with a coil of $1\, kW$ at $27 \,^oC$. The lid of the container is open and energy dissipates at rate of $160\, J/s$. In how much time temperature will rise from $27\,^oC$ to $77\,^oC$ $[$ Given specific heat of water is $4.2\, kJ/kg$ $]$