Question

equivalent resistance of two resistors when connected in series is 25 ohm . when the resistors are connected in parallel , their equivalent resistance is 4 ohm . calculate the value of resistance​

Answer 1

Given:

Equivalent resistance of two resistors when connected in series is 25 ohm, when the resistors are connected in parallel, their equivalent resistance is 4 ohm .

To find:

Value of resistances?

Calculation:

Let the resistances be x and y :

In series combination:

$\therefore \: x + y = 25$

In parallel combination:

$\therefore \: \dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{4}$

$\implies \: \dfrac{x + y}{xy} = \dfrac{1}{4}$

$\implies \: 4(x + y)= xy$

$\implies \: 4(25)= xy$

$\implies \: xy = 100$

$\implies \: x= \dfrac{100}{y}$

Putting value of x in eq.(1):

$\therefore \: x + y = 25$

$\implies \: \dfrac{100}{y} + y = 25$

$\implies \: \dfrac{100 + {y}^{2} }{y} = 25$

$\implies \: 100 + {y}^{2} = 25y$

$\implies \: {y}^{2} - 25y + 100= 0$

$\implies \: {y}^{2} - 20y - 5y+ 100= 0$

$\implies \: y(y - 20) - 5(y - 20)= 0$

$\implies \: (y- 5)(y - 20)= 0$

So, y = 5 or y = 20.

$\therefore \: x = \dfrac{100}{20} \: or \: \dfrac{100}{5} \\ \implies \: x = 5 \: or \: 20 \: ohm$

So, 2 combinations are possible:

• x = 5 ohm and y = 20 ohm
• x = 20 ohm and y = 5 ohm.