In an experiment to determine the temperature coefficient of resistance of a conductor,a coil of wire $X$ is immersed in a liquid. It is heated by an external agent. $A$ meter bridge setup is used to determine the resistance of the coil $X$ at different temperatures. The balancing points measured at temperatures $t_1=0^{\circ} C$ and $t_2=100^{\circ} C$ are $50 \ cm$ and $60 \ cm$ respectively. If the standard resistance taken out is $S=4 \ \Omega$ in both trials,the temperature coefficient of the coil is

  • A
    $0.05^{\circ} C^{-1}$
  • B
    $0.02^{\circ} C^{-1}$
  • C
    $0.005^{\circ} C^{-1}$
  • D
    $2.0^{\circ} C^{-1}$

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In a metre-bridge experiment,the balance point is obtained when the gaps are closed by $2 \Omega$ and $3 \Omega$ resistors. $A$ shunt of $x \Omega$ is added in parallel to the $3 \Omega$ resistor to shift the balance point by $22.5 \ cm$. The value of $x$ is: (in $\Omega$)

An unknown resistance $R_1$ is connected in series with a resistance of $10 \,\Omega$. This combination is connected to one gap of a meter bridge while a resistance $R_2$ is connected in the other gap. The balance point is at $50 \, cm$. Now,when the $10 \,\Omega$ resistance is removed,the balance point shifts to $40 \, cm$. The value of $R_1$ is (in $\Omega$):

If the null point of a meter bridge is obtained at $50 \ cm$,what will be the value of the unknown resistor $X$ if the known resistor $R$ is $10 \ \Omega$ (in $\Omega$)?

Assertion $(A):$ In a meter bridge experiment,the unknown resistance is placed inside an enclosure maintained at a higher temperature. The null point can be obtained at the same position as before by decreasing the value of the standard resistance.
Reason $(R):$ The resistance of a metal increases with an increase in temperature.

In a meter bridge experiment,the balance point is obtained if the gaps are closed by $2\,\Omega$ and $3\,\Omega$ resistors. $A$ shunt of $x\,\Omega$ is added to the $3\,\Omega$ resistor to shift the balancing point by $22.5\,cm$. The value of $x$ is $................$

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