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Two cells in series with a resistor: resistance for which one cell's terminal voltage is zero

This type of question, asked 3 times: 2021 Paper 8, 25 Jun 2022, 27 Jul 2022. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 8

    11
    Two cells of emf 2E2E and EE with internal resistance r1r_{1} and r2r_{2} respectively are connected in series to an external resistor RR (see figure). The value of RR, at which the potential difference across the terminals of the first cell becomes zero is

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  2. Question 2

    25 Jun 2022

    99
    Two cells of same emf but different internal resistances r1r_{1} and r2r_{2} are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is

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  3. Question 3

    27 Jul 2022

    11
    Two sources of equal emfs are connected in series. This combination is connected to an external resistance RR. The internal resistances of the two sources are r1r_{1} and r2(r1>r2)r_{2}\left( r_{1}>r_{2} \right). If the potential difference across the source of internal resistance r1r_{1} is zero then the value of RR will be

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