What is the impedance of a series circuit composed of resistance and reactance values of 25 ohms, 14 ohms, and 10 ohms?

To determine the impedance of a series circuit that consists of both resistive and reactive components, you need to apply the formula for calculating impedance (Z) in an AC circuit, which is represented as:

[

Z = \sqrt{R^2 + X^2}

]

where ( R ) is the resistance and ( X ) is the total reactance.

In this scenario, the circuit has a resistance of 25 ohms, and the reactance values are given as 14 ohms and 10 ohms. First, we need to find the total reactance ( X ) by summing the individual reactances:

[

X = 14 , \text{ohms} + 10 , \text{ohms} = 24 , \text{ohms}

]

With ( R = 25 ) ohms and ( X = 24 ) ohms, you can now plug these values into the impedance formula:

[

Z = \sqrt{25^2 + 24^2}

]

Calculating the squares:

[

25^2 = 625

]

[

24^2 = 576

]

Now, sum