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# a circuit has resistance R is connected to an similar cell if the current in the circuit is the same whether the cells are connected in series or in parallel then the internal resistance R of each cell given by,?

Samyak Jain
333 Points
2 years ago
Case 1. Resistance R is connected to n similar cells each of internal resistance r and emf E in series.
Equivalent emf of n identical cells in series = nE and equivalent resistance of the circuit = nr +R.
Let current in the circuit be i1.
By Ohm’s law, nE = i1(nr + R)  $\Rightarrow$  i1 = nE / (nr + R)          ...(1).
Case 2. Resistance R is connected to n similar cells each of internal resistance r and emf E.
The cells are connected in parallel.
Equivalent emf of n identical cells in parallel = E and equivalent resistance of the circuit = r/n +R.
Let current in the circuit be i2.
By Ohm’s law, E = i2(r/n + R)  $\Rightarrow$  i2 = E / (r/n + R) = nE / (r + nR)  ...(2).
It is given that i1 = i2.
From (1) and (2),  nE / (nr +R)  =  nE / (r + nR)  i.e.  1 / (nr +R)  =  1 / (r + nR).
nr + R  =  r + nR   $\Rightarrow$   (n – 1)r  =  (n – 1)R
$\therefore$  r = R.