Question

1) Derive expression emf of n cells in parallel. for equivalent Connected​

Answer 1

Explanation:

Let ε

1

and ε

2

be the emfs of the two cells connected in parallel.

Let r

1

and r

2

be their intermal resistance respectively

I

1

and I

2

are the currents leaving the positive electrodes of the cells.

At B

1

, currents I

1

and I

2

flow in whereas the current I flows out. Therefore I=I

1

+I

2

Let V

1

and V

2

be the potentials at B

1

and B

2

respectively.

P.d across the first cell is V

1

−V

2

=V=ε

1

−I

1

r

1

P.d across the second cell is also V

1

−V

2

=V=ε

1

−I

1

r

1

Hence I

1

=

r

1

ε

1

−V

and I

2

=

r

2

ε

2

−V

I=I

1

+I

2

=

r

1

ε

1

−V

+

r

2

ε

2

−V

I=

r

1

ε

1

−

r

1

V

+

r

2

ε

2

−

r

2

V

I=(

r

1

ε

1

+

r

1

ε

2

)−V(

r

1

V

+

r

2

V

)

I=

r

1

r

2

ε

1

r

2

+ε

2

r

1

−V(

r

1

r

2

r

1

+r

2

)

V(

r

1

r

2

r

1

+r

2

)=

r

1

r

2

ε

1

r

2

+ε

2

r

1

−I

V(r

1

+r

2

)=ε

1

r

2

+ε

2

r

1

−Ir

1

r

2

V=

r

1

+r

2

ε

1

r

2

+ε

2

r

1

−I(

r

1

+r

2

r

1

r

2

)