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An infinite ladder network of resistances is constructed with 1\Omega and 2\Omega resistances as shown in fig.Battery between A and B has negligible internal resistance.Current that passes through the 2\Omega resistance nearest to battery is

 

Option: 1

2A 


Option: 2

1.5A 


Option: 3

2A 


Option: 4

3A


Answers (1)

best_answer

The connection of battery and current distribution is shown the figure.

Resistance between A and B =\frac{2 \times 2}{2+2}=1 \Omega

Resistance between A{}' and B{}' = 2\Omega

\text { Current } \mathrm{i}=\frac{6 \text { volt }}{2 \Omega}=3 \mathrm{amp}

Potential difference across AB

\begin{aligned} & \mathrm{V}_{\mathrm{AB}}=\mathrm{R}_{\mathrm{AB}} \times \mathrm{i}=1 \times 3=3 \text { volt. } \\ & \therefore \mathrm{i}=\frac{V_{A B}}{R}=\frac{3 \mathrm{volt}}{2 \Omega}=1.5 \mathrm{amp} \end{aligned}

 

Posted by

Sanket Gandhi

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