n equal cell having emf E and internal resistance r, are connected in series circuit of a resistance R. Same current flows in circuit either they connected in series or parallel, if:

Options

A. `R=nr`
B. `R=r`
C. `r=nR`
D. `R=sqrt(n)r`

Answer

B

Explanation

Cells in series,
Current through the external resistance, `I=(n epsilon)/(R+nr)`
Cells in parallel, `I=(epsilon)/(R+(r)/(n))=(n epsilon)/(nR+r)`
According to problem, `(n epsilon)/(R+nr)=(n epsilon)/(nR+r)`
or, `R+nr=nR+rimpliesR(1-n)=r(1-n)impliesR=r`