Question

find equivalent resistance complete the answer​

Answer 1

Given : A circuit having 5 resistors of R Ω each.

To find : Equivalent resistance

Solution :

To solve this question, we should know about series and parallel connection of resistors.

Resistors are said to be in a series connection when they are connected from end to end and if the ending point of two or more resistors is connected from a single point, they are said to be in parallel connection.

In the given figure, we can see that resistors between joints AB and BC are in series connection and resistors between AD and DC are also in series connection whereas the combination of resistors between ADC and ABC is in parallel connection to resistor between AC.

Equivalent resistance in series connection can be expressed as::

• Equivalent resistance = R1 + R2 + R3... Rn

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Equivalent resistance in parallel connection can be expressed as::

• Equivalent resistance = 1/R1 + 1/R2 + 1/R3 ... 1/Rn

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Resistance in wire ABC is series connection::

⇒ Resistance in ABC = R1 + R2

⇒ Resistance in ABC = RΩ + RΩ

⇒ Resistance in ABC = 2 RΩ

Resistance in wire ADC is series connection::

⇒ Resistance in ADC = R1 + R2

⇒ Resistance in ADC = RΩ + RΩ

⇒ Resistance in ADC = 2 RΩ

The equivalent resistance between A and C is::

⇒ Equivalent resistance = 1/R1 + 1/R2 + 1/R3

⇒ Equivalent resistance = 1/(Resistance in ABC) + 1/(Resistance in ADC) + 1/(Resistance in AC)

⇒ Equivalent resistance = 1/2RΩ + 1/RΩ + 1/2Ω R

⇒ Equivalent resistance = 2 R Ω

So the total resistance between A and C is 2R Ω.