Question 396: Current Electricity

Question

A 9 V battery with internal resistance of 0.5 $\Omega $  is connected across an  infinite network as shown in the figure. All ammeters A
1
, A
2
,
3
and voltmeter V are ideal.
Choose correct statement.
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l83o2ean/4705580b-14b6-475f-a790-14f3b6309db4/d0b2c6f0-354b-11ed-8c5c-f3f0850e6b94/file-1l83o2eao.png?format=png)

Accepted Answer

Assume equivalent resistance of the infinite network is x.
The circuit can be redrawn like this,
Here 4 $\Omega $ and x $\Omega $ are parallel,
$	herefore\,\,\,$ ${1 \over {{x_{eq}}}}$ = ${1 \over 4}$ + ${1 \over x}$
$ \Rightarrow $$\,\,\,$ x
eq
= ${{4x} \over {4 + x}}$
$	herefore\,\,\,$ Equivalent resistance between point A and B is ,
x = ${{4x} \over {4 + x}}$ + 2
$ \Rightarrow $$\,\,\,$ x = $ {{8 + 6x} \over {4 + x}}$
$ \Rightarrow $$\,\,\,$ 4x + x
2
= 8 + 6x
$ \Rightarrow $$\,\,\,$  x
2
$-$ 2x $-$ 8 = 0
$ \Rightarrow $ $\,\,\,$ x = ${{2 \pm \sqrt {4 - 4\left( 1 ight)\left( { - 8} ight)} } \over 2}$
$ \Rightarrow $$\,\,\,$x = ${{2 \pm 6} \over 2}$
$ \Rightarrow $$\,\,\,$ =  4 $\Omega $
(as negative value of x is not acceptable)
$	herefore\,\,\,$ Reading of Aonmeter,  A
1
= ${V \over {R + r}}$
A
1
= ${9 \over {4\,\, + 0.5}}$ = 2 A
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l83o3jm4/9ec9cb27-fb68-445d-b397-81001e91889e/f09db4c0-354b-11ed-8c5c-f3f0850e6b94/file-1l83o3jm5.png?format=png)

Answer

Reading of A
1
is 2 A

Answer

Reading of A
1
is 18 A

Answer

Reading of   V   is  9 V

Answer

Reading of   V   is   7 V

Current Electricity

A 9 V battery with internal resistance of 0.5 \Omega is connected across an infinite network as shown in the figure. All ammeters A 1 , A 2 , 3 and voltmeter V are ideal. Choose correct statement.

Choose the correct answer: