Question

the total resistance of two resistors R1 and R2 when connected in series is 9 ohm and when connected in parallel is 2 ohm find R1 and R2​

Answer 1

Answer:

Explanation:

R1 +R2 = 9 ……………….(eq.1)

R1 = 9 - R2 …………(eq.2)

R1 × R2 ÷ (R1 + R2) = 2

R1.R2 ÷ 9 = 2 …(from eq.1)

R1.R2 = 18

R1 = 18 ÷ R2 ………………(eq.3)

From eq.2 & eq.3 , we get ,

9 - R2 = 18 ÷ R2

R2 ( 9 - R2 ) = 18

9R2 - R2^2 = 18

R2^2 - 9R2 + 18 = 0

R2^2 - 6R2 - 3R2 + 18 = 0

R2 ( R2 - 6 ) -3 ( R2 - 6 ) = 0

(R2–3)(R2–6) = 0

R2 = 3 ohm or R2 = 6 ohm

R1 = 9 – 3 or R1 = 9 - 6

R1 = 6 ohm or R1 = 3 ohm

This means when the value of Resistor 1 is 6 ohm then value of Resistor 2 will be 3 ohm and when the value of Resistor 1 is 3 ohm then the value of Resistor 2 will be 6 ohm.