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Question
What is the resistance between P and Q?
Options
\(\dfrac{3}{4} \Omega\)
\(\dfrac{4}{3} \Omega\)
\(\dfrac{16}{3} \Omega\)
infinity
MCQ
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Solution
\(\boldsymbol{\dfrac{16}{3}\,\Omega}\)
Explanation:
The two upper resistors of \(2\,\Omega\) each are connected in series.
\[ R_1=2+2\]
\[ =4\,\Omega \]
This combination is in parallel with the middle \(2\,\Omega\) resistor.
\[ R_2=\frac{4\times2}{4+2}\]
\[=\frac{8}{6}\]
\[=\frac{4}{3}\,\Omega \]
The two lower resistors of \(2\,\Omega\) each are in series with this combination.
\[ R=2+\frac{4}{3}+2 \]
\[ =\frac{6+4+6}{3} \]
\[ {{=\dfrac{16}{3}\,\Omega}} \]
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