To FIND:-

• The TOTAL EFFECTIVE resistance in the diagram provided.

Note:-

• It's NECESSARY to the label each resistor in a circuit. (As shown in the attachment)

Solution:-

From the attachment we have:-

• R₁ = 2Ω
• R₂ = 5Ω
• R₃ = 20Ω
• R₄ = 1Ω
• R₅ = 3Ω
• R₆ = 4Ω
• R₇ = 6Ω
• R₈ = 12Ω

Now,

Here we can see that:-

• Resistors R₂ and R₃ are parallel
• Resistors R₆, R₇ and R₈ are also parallel

Hence, Firstly let us find the effective resistance in the resistors connected in parallel combination.

We know,

Effective resistance in a circuit is represented as follows:-

For resistors R₂ and R₃:-

=>

=>

=>

=>

For resistors R₆, R₇ and R₈:-

=

=>

=>

=>

=>

Now,

From the second attachment we can see that resistors R₁, R₅ and Rₜ are in series.

Also, resistors R₁ and Rₚ are in series.

We know,

Effective resistance in series combination is represented by:-

• Rₛ = R₁ + R₂ . . . . . . . . . . . . Rₙ

Hence,

For resistors R₄, R₅ and Rₜ:-

=

=

For resistors R₁ and Rₚ:-

=

=

Finally,

The resistors and are parallel (See 3rd attachment).

Hence,

The effective resistance across the circuit is :-

=>

=>

=>

=>

∴ The effective resistance across the circuit is 3Ω.

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