The temperature coefficient of resistance of tungsten is $4.5 \times 10^{-3}{ }^{\circ} C ^{-1}$ and that of germanium is $-5 \times 10^{-2}{ }^{\circ} C ^{-1}$. A tungsten wire of resistance $100 \,\Omega$ is connected in series with a germanium wire of resistance $R$. The value of $R$ for which the resistance of combination does not change with temperature is .......... $\Omega$
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A battery of internal resistance $4$ $\Omega$ is connected to the network of resistances as shown. In order to give the maximum power to the network, the value of $R$ (in $\Omega $) should be
A potential divider is used to give outputs of $4\,V$ and $8\,V$ from a $12\,V$ source. Which combination of resistances, $(R_1 : R_2 : R_3)$ gives the correct voltages
The drift velocity of free electrons in a conductor is ‘$v$’ when a current ‘$i$’ is flowing in it. If both the radius and current are doubled, then drift velocity will be
A rod of length $l$ with thermally insulated lateral surface is made of a material whose thermal conductivity $K$ varies as $K = C/T$ , where $C$ is a constant. The ends are at temperatures $T_1$ and $T_2$ . The heat current density is
A potentiometer wire of length $1\,m$ and resistance $10\,\Omega$ is connected in series with a cell of $emf$ $2\,V$ with internal resistance $1 \,\Omega$ and a resistance box including a resistance $R$. If potential difference between the ends of the wire is $1\, mV$, the value of $R$ is ............. $\Omega $
A current of $3\,amp$ flows through the $2\,\Omega $ resistor shown in the circuit. The power dissipated in the $5\,\Omega $ resistor is ................. $watt$
The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is $0.25\, \Omega$. What will be the effective resistance if they are connected in series ? (In $\Omega$)
Three resistances of one ohm each are connected in parallel. Such connection is again connected with $\frac{2}{3}\,\Omega $ resistor in series. The resultant resistance will be ........... $\Omega$