Question

- Two cells of emf 2E and E and internal
resistances 2r and r respectively, are
connected in parallel. Obtain the
expressions for the equivalent emf and the
internal resistance of the combination.​

Answer 1

wo cells of EMF 1.5 volt and 2.0 volt having internal resistance is 0.2 ohm and 0.3 ohm respectively are connected in parallel calculate the EMF and internal resistance of the equivalent cell.

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Answer 2

Equivalent internal resistance is $\dfrac{2r}{3}$ and equivalent emf is $\dfrac{4E}{3}$ .

Given :

Two cells of emf 2E and E and internal  resistances 2r and r respectively, are

connected in parallel.

We know , When cells are in parallel their equivalent emf is :

$\dfrac{E_{eq}}{r_{eq}}=\dfrac{E_1}{r_1}+\dfrac{E_2}{r_2}$     ...( 1 )

Here $r_{eq}$ is given by :

$\dfrac{1}{r_{eq}}=\dfrac{1}{r_1}+\dfrac{1}{r_2}$

Putting value of resistance in above equation we get ,

$r_{eq}=\dfrac{2r}{3}$

Now , putting value of all these in equation 1 we get ,

$\dfrac{E_{eq}}{\dfrac{2r}{3}}}=\dfrac{2E}{2r}+\dfrac{E}{r}\\\\E_{eq}=\dfrac{4E}{3}$

Therefore , equivalent internal resistance is $\dfrac{2r}{3}$ and equivalent emf is $\dfrac{4E}{3}$ .

Hence , this is the required solution .

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Resistance

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