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Potentiometer with a resistance in the primary circuit: potential gradient, emf or resistance

This type of question, asked 4 times: 2021 Paper 14, 14 Jun 2022, 26 Jul 2022, 28 Jul 2022. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 14

    15
    In a potentiometer setup, EMF of primary cell is 6 V6\text{ }V and internal resistance is 20Ω20\Omega. The potentiometer wire is of length 10 m10\text{ }m having 0.1Ω/cm0.1\Omega/cm. This setup is used to find EMF of a cell which is balanced at 5.5 m5.5\text{ }m mark. Find EMF of the cell.

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  2. Question 2

    14 Jun 2022

    113
    A potentiometer wire of length 10 m10\text{ }m and resistance 20Ω20\Omega is connected in series with a 25 V25\text{ }V battery and an external resistance 30Ω30\Omega. A cell of emf EE in secondary circuit is balanced by 250 cm250\text{ }cm long potentiometer wire. The value of EE (in volt) is x10\frac{x}{10}. The value of xx is

  3. Question 3

    26 Jul 2022

    119
    A potentiometer wire of length 300 cm300\text{ }cm is connected in series with a resistance 780Ω780\Omega and a standard cell of emf 4 V4\text{ }V. A constant current flow through potentiometer wire. The length of the null point for cell of emf 20mV20mV is found to be 60 cm60\text{ }cm. The resistance of the potentiometer wire is ____\_\_\_\_ Ω\Omega.

  4. Question 4

    28 Jul 2022

    25
    As shown in the figure, a potentiometer wire of resistance 20Ω20\Omega and length 300 cm300\text{ }cm is connected with resistance box (R.B.) and a standard cell of emf 4 V4\text{ }V. For a resistance ' RR ' of resistance box introduced into the circuit, the null point for a cell of 20mV20mV is found to be 60 cm60\text{ }cm. The value of ' RR ' is ____\_\_\_\_ Ω\Omega.