Question

There are three resistors having 6 Q resistance each, a) In which way you will get the maximum effective resistance and how much is it? b) In which way you will get the minimum effective resistance and how much is it?
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Answer 1

Answer:

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Answer 2

ANSWER:

Given:

• 3 resistors of resistance 6 Ω each

To Find:

1. Way to get maximum effective resistance and its value.
2. Way to get minimum effective resistance and its value.

Solution:

1. MAXIMUM EFFECTIVE RESISTANCE

We know that, for resistors to give maximum effective resistance we need to  connect them in series.

In series connection, the resistance of each individual resistor gets added directly, resulting in a value with maximum effective resistance.

So,

⇒ R' = R₁ + R₂ + ... + Rₙ

Here, R' is effective resistance.

In question, we have 3 resistors, each of 6 Ω.

So,

⇒ R' = R₁ + R₂ + R₃

⇒ R' = 6 + 6 + 6

⇒ R' = 18Ω

Hence, the maximum resistance will be in series connection and the value will be 18Ω.

2. MINIMUM EFFECTIVE RESISTANCE

We know that, for resistors to give minimum effective resistance we need to connect them in parallel.

In parallel connection, the inverse of resistance of each individual resistor gets added, resulting in a value with minimum effective resistance.

So,

⇒ 1/R' = 1/R₁ + 1/R₂ + ... + 1/Rₙ

Here, R' is effective resistance.

In question, we have 3 resistors, each of 6 Ω.

So,

⇒ 1/R' = 1/R₁ + 1/R₂ + 1/R₃

⇒ 1/R' = 1/6 + 1/6 + 1/6

⇒ 1/R' = 3/6

⇒ 1/R' = 1/2

⇒ R' = 2Ω

Hence, the minimum resistance will be in parallel connection and the value will be 2Ω.