Question

Calculate the equal resistance between A and B​

Answer 1

Question :

Calculate the equivalent resistance between A and B ?

Answer

Given : -

There 4 resistors connected in a parallel series combination .

The resistance of the resistors are ;

0.5 ohm's , 2.6 ohm's , 3.5 ohm's , 8.6 ohm's.

Required to find : -

• Equivalent resistance between A and B ?

Formulae used : -

To find the equivalent resistance between any given n number of resistors which are connected in series is ;

$\boxed{\tt{ R_{eq } = R_1 + R_2 + R_3 \dots \dots }}$

To find the equivalent resistance between any given n number of resistors which are connected in parallel is ;

$\boxed{\tt{ \dfrac{1}{R_{eq }} = \dfrac{1}{ R_1 } + \dfrac{1}{R_2} + \dfrac{1}{R_3} \dots \dots }}$

Solution : -

There 4 resistors connected in a parallel series combination .

The resistance of the resistors are ;

0.5 ohm's , 2.6 ohm's , 3.5 ohm's , 8.6 ohm's.

We need to find the equivalent resistance between A and B .

So,

From the diagram we can conclude that ;

The resistors which are connected in between the points A and B are in parallel to each other.

Because, the potential difference across the points is constant.

But,

However,

The consecutive resistors are in series with each other .

i.e

0.5 ohm's resistor is in series with 2.6 ohm's resistor

Similarly,

8.6 ohm's resistor is in series 3.5 ohm's resistor

And,

The equivalent resistance of these two combinations are in parallel to each other .

Now,

Let's calculate the equivalent resistance between the points A and B .

So,

0.5 ohm's resistor is in series with 2.6 ohm's resistor

Using the formula ;

$\boxed{\tt{ R_{eq } = R_1 + R_2 + R_3 \dots \dots }}$

➟ Req = 0.5 ohm's + 2.6 ohm's

➟ Req = 3.1 ohm's

Similarly,

8.6 ohm's resistor is in series 3.5 ohm's resistor

Using the formula ;

➟ Req = 8.6 ohm's + 3.5 ohm's

➟ Req = 12.1 ohm's

Now,

These two equivalent resistances are in parallel to each other .

So,

Using the formula ;

$\boxed{\tt{ \dfrac{1}{R_{eq }} = \dfrac{1}{ R_1 } + \dfrac{1}{R_2} + \dfrac{1}{R_3} \dots \dots }}$

➟ 1/Req = 1/3.1 + 1/12.1

➟ 1/Req = 12.1 + 3.1/37.51

➟ 1/Req = 15.2/37.51

➟ Req = 37.51/15.2

➟ Req = 2.4677 . . . . . .

➟ Req = 2.5 ohm's ( approximately )

Therefore,

Equivalent resistance between points A and B is 2.5 ohm's ( appxo. )