Question

The equivalent resistance of series combination of two resistors is 's'. When they are connected in parallel, the equivalent resistance is 'p'. If s = np, then the minimum value for n is ______. (Round off to the Nearest Integer)

Options

• 1

• 2

• 3

• 4

Answer 1

The equivalent resistance of series combination of two resistors is 's'. When they are connected in parallel, the equivalent resistance is 'p'. If s = np, then the minimum value for n is 4. (Round off to the Nearest Integer)

Explanation:

Equivalent resistance in series, s = R₁ + R₂

Equivalent resistance in parallel P = `("R"_1"R"_2)/("R"_1+"R"_2)`

Given (R₁ + R₂) = n `("R"_1"R"_2)/("R"_1+"R"_2)`

⇒ `"R"_1^2+"R"_2^2+2"R"_1"R"_2="nR"_1"R"_2`

⇒ `"R"_1^2/("R"_1"R"_2)+("R"_2^2)/("R"_1"R"_2)+2="n"`

⇒ `"R"_1/"R"_2+"R"_2/"R"_1+2="n"`

Let `"R"_1/"R"_2=alpha`

Then, `alpha+1/alpha+2="n"`

⇒ α² + α(2 - n) + 1 = 0 

for real value of 'α'

(2 - n)² - 4 ≥ 0

for minimum value (2 - n)² - 4 = 0

⇒ n = 0 or n = 4

⇒ n = 4 [∵ n ≠ 0]