Question

we have four resistances of 1 ohm 2 ohm 3 ohm and 4 ohm how they should be connected so we can obtain a combination such that its equivalent resistance is less than the minimum value present in the combination No spam pls !!!!!!!!

Answer 1

Given : -

Four resistors of resistance 1 ohm , 2 ohm , 3 ohm & 4 ohm

Required to find : -

The combination in which the equivalent resistance is less than the minimum value of the resistance of the resistor ?

Important formulae : -

Formula to find the equivalent resistance when it is connected in series .

$\boxed{\sf{ {R}_{eq} = {R}_{1} + {R}_{2} + {R}_{3} \dots \dots }}$

Formula to find the equivalent resistance when it is connected in parallel .

$\boxed{\sf{ \dfrac{1}{ {R}_{eq} } = \dfrac{ 1}{ {R}_{1} } +\dfrac{1}{{R}_{2}} + \dfrac{1}{ {R}_{3} } \dots \dots }}$

Solution : -

Four resistors of resistance 1 ohm , 2 ohm , 3 ohm & 4 ohm

we need to find the combination in which the equivalent resistance is less than the minimum value of the resistance of the resistor ?

As we know that ;

There is are 2 combination in which resistors can be arranged .

• 1 ) Series connection

• 2 ) Parallel connection

In some cases , we will given a circuit which consists of only parallel connection or series connection or both series and parallel connection .

The equivalent resistance of the resistors which are connected in series have an equivalent resistance which is greater than the individual resistance .

Whereas ,

The equivalent resistance of the resistors which are connected in parallel have an equivalent resistance which is less than the individual resistance .

So,

From this we can conclude that ;

The resistors of 1 ohm , 2 ohm , 3 ohm & 4 ohm when connected in series has an equivalent resistance which is greater than its individual resistance whereas when the resistors are connected in parallel the equivalent resistance will be less than the individual resistance .

Therefore,

Parallel combination is the combination in which the resistors should be arranged . so that the equivalent resistance is less than Individual resistance .

Additional Information : -

How to identify whether the given circuit has a parallel combination or series combination ?

Answer : -

The potential difference across the 2 ends of the resistors will be equal / constant .

whereas,

In a series combination the potential between the 2 ends of the resistors will be different / unequal .

Answer 2

$\blue{\bold{\underline{\underline{Solution:-}}}}$

You should connect the resistances in a parallel circuit.

Equivalent Resistance = $\bf\green{\frac{1}{R _{1}} + \frac{1}{R _{2} } + \frac{1}{R _{3}} + \frac{1}{R _{4}} \: \: .....}$

Therefore it will be less than the minimum value present in the combination.

$\bf\blue{Hope\ it\ helps.}$

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