Question:
A \(9\ \mathrm{V}\) battery with internal resistance of \(0.5\ \Omega\) is connected across an infinite network as shown in the figure. All ammeters \(A_1, A_2, A_3\) and voltmeter \(V\) are ideal.
Choose correct statement.
A \(9\ \mathrm{V}\) battery with internal resistance of \(0.5\ \Omega\) is connected across an infinite network as shown in the figure. All ammeters \(A_1, A_2, A_3\) and voltmeter \(V\) are ideal.
Choose correct statement.
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Find the equivalent resistance of the infinite ladder (each section: \(1\ \Omega + 1\ \Omega\) in series, \(4\ \Omega\) shunt) using \(R=2+\frac{4R}{4+R}\).
Updated On: Nov 11, 2026
- Reading of \(A_1\) is \(2\ \mathrm{A}\)
- Reading of \(A_1\) is \(18\ \mathrm{A}\)
- Reading of \(V\) is \(9\ \mathrm{V}\)
- Reading of \(V\) is \(7\ \mathrm{V}\)
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The Correct Option is A
Solution and Explanation
Each repeating section has \(1\ \Omega\) (top) + \(1\ \Omega\) (bottom) in series and a \(4\ \Omega\) rung (ideal ammeters have zero resistance). Let the infinite network have resistance \(R\): \(R=2+\frac{4R}{4+R}\Rightarrow R^2-2R-8=0\Rightarrow R=4\ \Omega\).
Total resistance \(=4+0.5=4.5\ \Omega\), so the current through \(A_1\) is \(I=\frac{9}{4.5}=2\ \mathrm{A}\).
The voltmeter reads the terminal voltage \(=9-2\times0.5=8\ \mathrm{V}\) (so options (3) and (4) are wrong), and \(A_1\) reads \(2\ \mathrm{A}\).
Answer: (1) Reading of \(A_1\) is \(2\ \mathrm{A}\)
Total resistance \(=4+0.5=4.5\ \Omega\), so the current through \(A_1\) is \(I=\frac{9}{4.5}=2\ \mathrm{A}\).
The voltmeter reads the terminal voltage \(=9-2\times0.5=8\ \mathrm{V}\) (so options (3) and (4) are wrong), and \(A_1\) reads \(2\ \mathrm{A}\).
Answer: (1) Reading of \(A_1\) is \(2\ \mathrm{A}\)
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