Assume a hypothetical wire in which free electron density changes with temperature in proportionality $n\ \alpha \ T$ assuming $\tau $(Relaxation time of collision) and dimensions of wire remain unchanged with increasing temperature. Which one of the resistance $v/s$ temperature graph is true
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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:
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
To measure the internal resistance of a battery, potentiometer is used. For $\mathrm{R}=10 \Omega$, the balance point is observed at $\ell=500 \mathrm{~cm}$ and for $\mathrm{R}=1 \Omega$ the balance point is observed at $\ell=400 \mathrm{~cm}$. The internal resistance of the battery is approximately :
In a potentiometer experiment the balancing with a cell is at length $240\, cm$. On shunting the cell with a resistance of $2$ $\Omega$, the balancing length becomes $120\, cm$. The internal resistance of the cell is ................. $\Omega $
Two resistors of resistance, $100\,\Omega$ and $200\,\Omega$ are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in $100\,\Omega$ to that in $200\,\Omega$ in a given time is:
A $5\, V$ battery with internal resistance $2\, \Omega$ and a $2\,V$ battery internal resistance $1\, \Omega$ are connected to a $10\, \Omega$ resistor as shown in the figure. The current in the $10\, \Omega$ resistor is :-
The circuit shown in the figure consists of a battery of $emf$ $\varepsilon = 10 \,V$ ; a capacitor of capacitance $C = 1.0$ $ \mu F$ and three resistor of values $R_1 = 2$ $\Omega$ , $R_2 = 2$ $\Omega$ and $R_3 = 1$ $\Omega$ . Initially the capacitor is completely uncharged and the switch $S$ is open. The switch $S$ is closed at $t = 0.$