\( n \) identical cells, each of e.m.f \( E \) and internal resistance \( r \), are connected in series. Later on, it was found that two cells ‘X’ and ‘Y’ are connected in reverse polarities. Calculate the potential difference across the cell ‘X’.

Question

In a meter bridge experiment, a resistance of \( 10 \, \Omega \) is balanced by a resistance \( X \) with a balance point at \( 40 \, \mathrm{cm} \). What is the value of \( X \)?

Answer 1

When \( n \) identical cells are connected in series, the total effective e.m.f. is given by: \[ E_{\text{total}} = nE \]. If two cells are connected with reverse polarity, their individual e.m.f.s subtract from the total e.m.f., resulting in: \[ E'_{\text{total}} = (n-2)E \]. Consequently, the potential difference across a single reversed cell 'X' equals the sum of the e.m.f.s of the two reversed cells: \[ V_X = 2E \]. Therefore, the potential difference across cell 'X' is \( 2E \).

\( n \) identical cells, each of e.m.f \( E \) and internal resistance \( r \), are connected in series. Later on, it was found that two cells ‘X’ and ‘Y’ are connected in reverse polarities. Calculate the potential difference across the cell ‘X’.

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