Question

When three equal resistors are connected in series, their resultant resistance is 15 ohms. When they are connected in parallel, their equivalent resistance will be, a) 5/3 Ohms b) 5 Ohms c) 15 Ohms d) 3/5 Ohms

Answer 1

Given:-

• Three equal resistances are connected in series.
• The net resistance is 15Ω .

To Find:-

• The net resistance when they are connected in parallel.

Formulae Used:-

When n resistances are connected in series ,

$\large{\underline{\boxed{\red{\sf{\dag R_{net}=R_1+R_2+R_3+.......+R_n }}}}}$

When n resistances are in parallel ,

$\large{\underline{\boxed{\red{\sf{\dag \dfrac{1}{R_{net}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+.......+\dfrac{1}{R_n }}}}}}$

Calculation:-

Let the resistance of each resistor be R , Then ,

Atq ,

➥ R + R + R = 15Ω .

➥ 3R = 15Ω.

➥ R = 15Ω/3.

➤ R = 5Ω.

Now , if these are connected in parallel , then :

➥ 1/R = 1/5Ω + 1/5Ω + 1/5Ω.

➥ 1/R = 1+1+1 / 5Ω .

➥ 1/R = 3/5Ω.

➤ R = 5Ω/3 .

Hence the net resistance in parallel is 5Ω/3.