$\"\"$

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Step 1:

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Observe the circuit.

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The resistors $\"\"$ , $\"\"$ and $\"\"$ form a T network.

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Convert the T network into a Pi network.

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Formula for the resistors when the $\"\"$ network is changed into $\"\"$ network.

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$\"\"$

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$\"\"$

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$\"\"$

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Here $\"\"$ , $\"\"$ and $\"\"$ .

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From the above formula :

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Step 2:

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Redraw the circuit replacing T network by a Pi network.

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$\"\"$

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The Resistance $\"\"$ and $\"\"$ are in parallel.

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The resultant parallel resistance is $\"\"$ .

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$\"\"$

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The resultant parallel resistance is $\"\"$ .

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The Resistance $\"\"$ and $\"\"$ are in parallel.

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The resultant parallel resistance is $\"\"$ .

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$\"\"$

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The resultant parallel resistance is $\"\"$ .

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The resistance $\"\"$ and $\"\"$ are in series.

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$\"\"$

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$\"\"$ .

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The resultant series resistance is $\"\"$ .

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Step 3:

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Redraw the circuit replacing the resistors $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ by $\"\"$ .

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$\"\"$

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The Resistance $\"\"$ and $\"\"$ are in parallel.

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The resultant parallel resistance is $\"\"$ .

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$\"\"$

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The resultant parallel resistance is $\"\"$ .

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The Resistance $\"\"$ and $\"\"$ are in parallel.

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The resultant parallel resistance is $\"\"$ .

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$\"\"$

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The resultant parallel resistance is $\"\"$ .

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The resistance $\"\"$ and $\"\"$ are in series.

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$\"\"$

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$\"\"$ .

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The Resistance $\"\"$ and $\"\"$ are in parallel.

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The resultant parallel resistance is $\"\"$ .

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$\"\"$

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$\"\"$ .

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Solution :

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The total resistance between A and B is $\"\"$ .