Question

When two resistors are in series they have values 25Ω and in parallel have value 4Ω. Find the value of each resistance.​

Answer 1

Answer:

5Ω and 20Ω

Explanation:

let the 2 resistors be 'xΩ' and 'yΩ'

When two resistors are in series they have values 25Ω

⇒ x + y = 25 ---(1)

⇒ y = 25 - x ---(2)

When two resistors are in parallel they have values 4Ω

⇒ $\frac{1}{4} = \frac{1}{x} + \frac{1}{y}$

⇒ $\frac{1}{4} = \frac{x + y}{xy}$

⇒ $\frac{1}{4} = \frac{25}{xy}$  ( from equation 1)

⇒ xy = 100

⇒ x(25 - x) = 100 (from equation 2)

⇒ 25x - x² = 100

⇒ x² - 25x + 100 = 0

⇒ x² - 20x - 5x + 100 = 0

⇒ x(x - 20) - 5(x - 20) = 0

⇒ (x -20)(x - 5) = 0

⇒ x = 5 (or) 20

⇒ y = 20 (or) 5   (from equation 2)

∴ the resistors are 5Ω and 20Ω

===============================================================

VERIFICATION:

2 resistors 5Ω and 20Ω

(i) when they are connected in series

   Effective resistance = 5 + 20 = 25Ω

(ii) when they are connected in parallel

   1/(Effective resistance) = $\frac{1}{5} + \frac{1}{20}$

   ⇒  1/(Effective resistance) = $\frac{4 + 1}{20}$

   ⇒  1/(Effective resistance) = $\frac{5}{20}$

   ⇒  Effective resistance = $\frac{20}{5}$

   ⇒  Effective resistance = 4Ω

===============================================================  

PLEASE MAKE MY ANSWER AS BRAINLIEST SO I CAN PROMOTE TO GENIUS RANK