(C) For two identical batteries with e.m.f. $E$ and internal resistance $r$ connected in parallel,the equivalent e.m.f. $E_{eq}$ is given by $E_{eq} =

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$(ii)$ is correct but $(i)$ is wrong.

(C) For two identical batteries with e.m.f. $E$ and internal resistance $r$ connected in parallel,the equivalent e.m.f. $E_{eq}$ is given by $E_{eq} = E$.Since $E_{eq} = E$,statement $(i)$ is incorrect because the equivalent e.m.f. is equal to the e.m.f. of either battery,not smaller.The equivalent internal resistance $r_{eq}$ for two resistors in parallel is given by $\frac{1}{r_{eq}} = \frac{1}{r} + \frac{1}{r} = \frac{2}{r}$,which implies $r_{eq} = \frac{r}{2}$.Since $\frac{r}{2} Therefore,$(ii)$ is correct but $(i)$ is wrong.

Class 12 Physics Current Electricity Electric Cells and Combination of cells in Series and Parallel

Easy

Two non-ideal identical batteries are connected in parallel. Consider the following statements:
$(i)$ The equivalent e.m.f. is smaller than either of the two e.m.f.s.
$(ii)$ The equivalent internal resistance is smaller than either of the two internal resistances.

A
Both $(i)$ and $(ii)$ are correct.
B
$(i)$ is correct but $(ii)$ is wrong.
C
$(ii)$ is correct but $(i)$ is wrong.
D
Both $(i)$ and $(ii)$ are wrong.

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Current Electricity

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Electric Cells and Combination of cells in Series and Parallel

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Two non-ideal identical batteries are connected in parallel. Consider the following statements:$(i)$ The equivalent e.m.f. is smaller than either of the two e.m.f.s.$(ii)$ The equivalent internal resistance is smaller than either of the two internal resistances.

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Two cells are connected in opposition as shown. Cell $E_1$ has an electromotive force (emf) of $8 \ V$ and an internal resistance of $2 \ \Omega$; cell $E_2$ has an emf of $2 \ V$ and an internal resistance of $4 \ \Omega$. The terminal potential difference of cell $E_2$ is: (in $V$)

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For a cell,the terminal potential difference $(P.D.)$ is $2.2\;V$ when the circuit is open and reduces to $1.8\;V$ when the cell is connected to an external resistance of $R = 5\;\Omega$. Determine the internal resistance $(r)$ of the cell.

$100$ cells, each of $e.m.f.$ $5\, V$ and internal resistance $1\, \Omega$, are to be arranged to produce maximum current in a $25\, \Omega$ external resistance. Each row must contain an equal number of cells. The number of rows should be:

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Two non-ideal identical batteries are connected in parallel. Consider the following statements:
$(i)$ The equivalent e.m.f. is smaller than either of the two e.m.f.s.
$(ii)$ The equivalent internal resistance is smaller than either of the two internal resistances.