Question

there are three resistance r1 r2 r3 .how they are conected to get minimum and maximum resistance ​

Answer 1

Answer: For minimum resistance, in parallel.

For maximum resistance, in series.

Explanation: We know that, resultant series resistance is

R = R1+ R2 + R3 +...... And so on

For parallel, it is

1/R = 1/R1+ 1/R2+ 1/R3 +......

On introspection we get to know this wonderful point about series and parallel combinations:-

• In series combination, resultant is always greater than the greatest resistance. (Obviously, it is sum of individual resistances)

• In parallel, it is always 'lesser' than the least resistance. (As it is harmonic mean of all the resistances in the circuit.)

You can check it with various combinations too, and you would conclude the same result.

Answer 2

Answer:

Given:

3 resistors have been supplied to us , namely r1 , r2, r3.

To find:

Arrangements that will lead to minimumband maximum equivalent resistance.

Concept:

Broadly speaking, we have 2 main type of arrangement of resistances :

• Series combination
• Parallel combination

In series combination , the resistances are connected end to end , whereas in parallel combination , the resistances are attached to same potential drops.

Calculation:

In series combination, we shall get Maximum equivalent resistance :

$\boxed{ \bold{R eq. = r1 + r2 + r3 }}$

In parallel combination , we shall get minimum equivalent resistance :

$\dfrac{1}{R \: eq.} = \dfrac{1}{r1} + \dfrac{1}{r2} + \dfrac{1}{r3}$

$\boxed{ \bold{R eq. = \dfrac{(r1)(r2)(r3)}{(r1)(r2) + (r2)(r3) + (r3)(r1)} }}$