Question

What is the minimum resistance that can be made using four resistors each
of 20 ?
OR
How many 10  resistors are to be connected in parallel to obtain
equivalent resistance of 2.5 ?​

Answer 1

(1)

Given :

• R 1 = R 2 = R 3 = R4 = R= 20 Ω

How to solve :

• In order to find the minimum equivalent resistance all the 4 resistors must be connected in parallel to each other .

Solution :

Equivalent resistance when n no of resistances are connected in parallel combination ,

$\implies\mathtt{1 / Rp = 1 / R 1 + 1/ R 2 +.. 1 / Rn }$

Hence ,

⇒ 1 / Rp = 1 / R + 1 / R + 1/ R + 1 /R

⇒ 1 / Rp = 4 / R

⇒ Rp = R / 4

⇒ Rp = 20 / 4

⇒ Rp = 5 Ω

The equivalent resistance of the combination is 5 Ω.

(2)

Given :

• Resistance of each resistor = R = 10Ω

• Equivalent resistance (Rp ) = 2.5 Ω

Solution :

Equivalent resistance when n no of resistances each of resistance R are connected in parallel combination ,

⇒ Rp = R / n

Now let's substitute the given values in the above equation ,

⇒ 2.5 = 10 / n

⇒ n = 10 / 2.5

⇒ n = 4