The combined resistance in the given circuit is $$5 \Omega.$$ What is the value of R ?

Question

The combined resistance in the given circuit is 5 Omega- What is the value of R -

Toppr Admin · Accepted Answer

In parallel combination of resistances- equivalent resistance is given by-dfrac-1-R- - -dfrac-1-R-1- - -dfrac-1-R-2-hence -dfrac-1-5- - -dfrac-1-10- - -dfrac-1-R-2-therefore -dfrac-1-R-2- - -dfrac-1-5- - -dfrac-1-10- -therefore R-2 - 10-160- - -Omega-

The combined resistance in the given circuit is $$5 \Omega.$$ What is the value of R ?

In parallel combination of resistances, equivalent resistance is given by,$$\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2}$$hence $$\dfrac{1}{5} = \dfrac{1}{10} + \dfrac{1}{R_2}$$$$\therefore \dfrac{1}{R_2} = \dfrac{1}{5} - \dfrac{1}{10}$$$$ \therefore R_2 = 10 \ \Omega$$

In parallel combination of resistances, equivalent resistance is given by,

$$\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2}$$

hence $$\dfrac{1}{5} = \dfrac{1}{10} + \dfrac{1}{R_2}$$

$$\therefore \dfrac{1}{R_2} = \dfrac{1}{5} - \dfrac{1}{10}$$

$$ \therefore R_2 = 10 \ \Omega$$