Question

six identical cells of EMF E and internal resistance R are connected in parallel and then the net EMF and internal resistance of the combination will be

Answer 1

Concept:

A conductor's ability to resist the flow of electric current through it is known as resistance.

The combination is referred to as a parallel combination when two or more resistances are coupled between the same two sites.

Given:

Six identical cells of emf E and internal resistance R are connected in parallel combination

Find:

The net emf and internal resistance of the combination.

Solution:

When n number of cells of the same emf and internal resistance are connected in parallel combination in the circuit,  then the net emf will be equal to the emf of a single cell.

$E_{net}=\frac{\frac{E_1}{r_1}+\frac{E_2}{r_2} +\frac{E_3}{r_3} +\frac{E_4}{r_4}+\frac{E_5}{r_5}+\frac{E_6}{r_6}}{\frac{1}{r_1} +\frac{1}{r_2} +\frac{1}{r_3} +\frac{1}{r_4} +\frac{1}{r_5} +\frac{1}{r_6} }$

$E_{net}=\frac{6(\frac{E}{R} )}{\frac{6}{R} }$

$E_{net}=E$

Now, as the resistances of the emf are connected in parallel combination.

$\frac{1}{r_{eq}}=\frac{1}{R} +\frac{1}{R} +\frac{1}{R}+ \frac{1}{R}+ \frac{1}{R}+ \frac{1}{R}$

$\frac{1}{r_{eq}}=\frac{6}{R}$

$r_{eq}=\frac{R}{6}$

The net emf and internal resistance of the combination is $E$ and $\frac{R}{6}$ respectively.

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