The net resistance of two resistors R1 and R2 connected in series is 8 ohm and their net resistance in parallel is 2ohm. What are the values of individual resistances R1 and R2, respectively?

Correct option is B

The correct answer is (b) 4 ohm; 4 ohm.
Explanation:
· Given: Rseries $$=R₁ + R₂ = 8$$​ ohm Rparallel = $$=\frac{(R₁ × R₂)}{(R₁ + R₂)} = 2$$​ ohm
· Substituting $$R₁ + R₂ = 8$$ ohm into the parallel resistance formula: $$\frac{(R₁ × R₂)}{8} = 2 → R₁ × R₂ = 16$$​
· Solving the quadratic equation $$x² - 8x + 16 = 0$$ : $$x = 4$$​ and $$x = 4$$​
· Therefore,$$R₁ = 4$$​ ohm and $$R₂ = 4$$​ ohm.
Information Booster
· Series combination: Total resistance is the sum of all resistances: Rtotal $$= R₁ + R₂ + …$$​
· Parallel combination: Total resistance is given by: Rtotal $$= \frac{1}{(\frac{1}{R₁} + \frac{1}{R₂ +} …)}$$ 
· For series: Rseries$$= R₁ + R₂$$​
· For parallel: Rparallel$$= \frac{(R₁ × R₂)}{(R₁ + R₂)}$$​
 Applications:

• Series connections are used for uniform current flow in circuits.
  
• Parallel connections are used in household wiring to ensure constant voltage.
  
•  Practical example: Designing resistive circuits in electronic devices like TVs and radios.