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What is the total current when an 'n' number of cells are connected in parallel? (Where 'E' is the EMF and 'R' is the internal resistance of each cell
Question

What is the total current when an 'n' number of cells are connected in parallel? (Where 'E' is the EMF and 'R' is the internal resistance of each cell)

A.

E/nR

B.

E/R

C.

nE/R

D.

E/(n + R)

E.

ER/n

Correct option is C

When cells are connected in parallel: The voltage (EMF) across all branches remains the same. The internal resistances behave like parallel resistors.So, the net internal resistance Req becomes:1Req=1R+1R+1R++1R=nR=>Req=RnThe total EMF of all parallel cells =E (since they are identical).Total Current (I):By Ohm’s Law:I=EReq=ER/n=nER\text{When cells are connected in \textbf{parallel}:} \\\quad \bullet\ \text{The \textbf{voltage (EMF)} across all branches remains the \textbf{same}.} \\\quad \bullet\ \text{The \textbf{internal resistances} behave like \textbf{parallel resistors}.} \\[10pt]\text{So, the \textbf{net internal resistance} } R_{\text{eq}} \text{ becomes:} \\\frac{1}{R_{\text{eq}}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \cdots + \frac{1}{R} = \frac{n}{R} \Rightarrow R_{\text{eq}} = \frac{R}{n} \\[10pt]\text{The total EMF of all parallel cells } = E \text{ (since they are identical).} \\[20pt]\textbf{Total Current (I):} \\\text{By Ohm’s Law:} \\I = \frac{E}{R_{\text{eq}}} = \frac{E}{R/n} = \frac{nE}{R}​​

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