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.

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

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: