In a potentiometer arrangement,$E_1$ is the cell establishing the current in the primary circuit,$E_2$ is the cell to be measured,$AB$ is the potentiometer wire,and $G$ is a galvanometer. Which of the following are the essential conditions for a balance point to be obtained?

  • A
    The $emf$ of $E_1$ must be greater than the $emf$ of $E_2$.
  • B
    Either the positive terminals of both $E_1$ and $E_2$ or the negative terminals of both $E_1$ and $E_2$ must be joined to one end of the potentiometer wire.
  • C
    The positive terminals of $E_1$ and $E_2$ must be joined to one end of the potentiometer wire.
  • D
    Both $(A)$ and $(B)$.

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In the given potentiometer circuit,the length of the wire $AB$ is $3 \, m$ and its resistance is $R = 4.5 \, \Omega$. The length $AC$ for no deflection in the galvanometer is ............... $m$.

The $e.m.f.$ of a standard cell balances across $150 \ cm$ length of a potentiometer wire. When a resistance of $2 \ \Omega$ is connected as a shunt across the cell,the balance point is obtained at $100 \ cm$. The internal resistance of the cell is .............. $\Omega$.

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$A$ wire of length $10 \ cm$ is connected to a cell of $emf$ $2 \ V$ and negligible internal resistance. The resistance of the wire is $3 \ \Omega$. The value of the series resistance required to obtain a potential gradient of $10 \ mV/cm$ is ................ $\Omega$.

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Explain the method to measure the internal resistance of a cell using a potentiometer.

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