Question

36 cells each of emf 8v are used in mixed grouping to send a maximum current through an external resistance 4 ohm. internal resistance of each cell is 1 ohm. The maximum current is
​

Answer 1

First of all, let's find the equivalent EMF of all the cells together.

• Since all the cells are placed with same polarities and in series, the equivalent potential difference will be :

$V_{eq} = 8 + 8 + ... \: 36 \: times$

$\implies V_{eq} = 8 \times 36$

$\implies V_{eq} = 288 \: volts$

And internal resistance in total is :

$r = 1 + 1 + ...36 \: times$

$\implies \: r = 1 \times 36$

$\implies \: r = 36 \: ohm$

Now, max current is :

$i = \dfrac{voltage}{r +R }$

$\implies \: i = \dfrac{288}{36 + 4}$

$\implies \: i = \dfrac{288}{ 40}$

$\implies \: i = 7.2 \: amp$

So, max current is 7.2 Amperes.

Answer 2

Explanation:

Since all the cells are placed with same polarities and in series, the equivalent potential difference will be :

V_{eq} = 8 + 8 + ... \: 36 \: timesV

eq

=8+8+...36times

\implies V_{eq} = 8 \times 36⟹V

eq

=8×36

\implies V_{eq} = 288 \: volts⟹V

eq

=288volts

And internal resistance in total is :

r = 1 + 1 + ...36 \: timesr=1+1+...36times

\implies \: r = 1 \times 36⟹r=1×36

\implies \: r = 36 \: ohm⟹r=36ohm

Now, max current is :

i = \dfrac{voltage}{r +R } i=

r+R

voltage

\implies \: i = \dfrac{288}{36 + 4} ⟹i=

36+4

288

\implies \: i = \dfrac{288}{ 40} ⟹i=

40

288

\implies \: i = 7.2 \: amp⟹i=7.2amp

So, max current is 7.2 Amperes.