Question

Three equal resistances, when combined in series have
equivalent resistance of 90. Their equivalent resistance
when combined in parallel will be​

Answer 1

Given :

Equivalent resistance of three equal resistors when they are connected in series is 90Ω.

To Find :

Their equivalent resistance when they are connected in parallel.

Solution :

A] Series connection :

Let resistance of each resistor be R$.$

Equivalent resistance of series is given by,

➙ Rs = R₁ + R₂ + R₃

➙ 90 = R + R + R

➙ 90 = 3R

➙ R = 90/3

➙ R = 30 Ω

B] Parallel connection :

Equivalent resistance of parallel is given by,

➙ 1/Rp = 1/R₁ + 1/R₂ + 1/R₃

➙ 1/Rp = 1/R + 1/R + 1/R

➙ 1/Rp = 3/R

➙ Rp = R/3

➙ Rp = 30/3

➙ Rp = 10 Ω

Answer 2

$\huge \bf {Question}$

Three equal resistances, when combined in series have

equivalent resistance of 90. Their equivalent resistance

when combined in parallel will be -

$\huge \bf {Answer}$

Given:-

Three equal resistances, when combined in series have

equivalent resistance of 90.

To Find:-

Their equivalent resistance when combined in parallel.

Resistance in Series Connection

Let, the resistance of each resistors be R

Equivalent resistance is given by each resistor in series combination,

$\bf {Rs = {R}_{1} + R₂ + R₃}$

$\bf {90 = R + R + R}$

$\bf {90 = 3R}$

$\bf \frac {90}{3} = R$

$\fbox \green {R = 30 Ω}$

Resistance in Parallel Connection

Equivalent resistance in parallel combination,

$\Large \bf \frac{1}{Rp} = \frac{1}{{R}_{1}} + \frac{1}{R₂} + \frac{1}{R₃}$

$\Large \bf \frac{1}{Rp} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R}$

$\Large \bf \frac{1}{Rp} = \frac{3}{R}$

$\large \bf Rp = \frac{R}{3}$

Substitute the value of R

$\large \bf Rp = \frac{30}{3}$

$\fbox \green {Rp = 10 Ω}$

Know more...!

Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω). Ohms are named after Georg Simon Ohm (1784-1854), a German physicist who studied the relationship between voltage, current and resistance.