Question

The power factor of a circuit in which a box having unknown electrical devices connected in series with a resistor of resistance 3 is 3/5. The reactance of the box is

Answer 1

Given:  a box having unknown electrical devices connected in series with a resistor of resistance 3 is 3/5.

To Find: The reactance of the box is

Solution:

In electrical circuits power factor of a circuit is defined as ratio of  true power to the apparent power.

It can also be defined as : resistance/ impedance.

power factor is expressed as:

                                    cosФ = $\frac{R}{Z}$    .................(eqn 1)

                     

                      Here, cosФ = $\frac{3}{5}$   ............  (given)

                                       R = 3

                      put the value of cosФ and R in (eqn 1), we get

                                       $\frac{3}{5}$ = $\frac{3}{Z}$

                                       Z = 5

so, R = 3, Z = 5

impedance is written as Z = R + jX   ................(eqn 2)

here, Z = impedence, R= resistance, X = reactance

eqn 2 can be written as

                                        Z = √R² + X²

                                        Z² = R² + X²

                                        5² =  3² + X²

                                        25 = 9 + X²

                                         X² = 16

                                          X = 4

So reactance is 4.

Answer: The reactance of the box is 4