Final answer:
To find the frequency at which an RL circuit with a resistance of 150Ω and inductance of 50mH has an impedance of 200Ω, calculate the inductive reactance using the impedance formula and solve for frequency using the inductive reactance formula.
Step-by-step explanation:
The frequency at which an RL circuit with a resistance of 150Ω (ohms) and an inductance of 50mH (millihenrys) will have an impedance of 200Ω can be found using the formula for impedance in an RL circuit:
Z = √(R^2 + (XL)^2)
Where:
- Z is the impedance
- R is the resistance
- XL is the inductive reactance, XL = 2πfL
Given the impedance (Z) of 200Ω and the resistance (R) of 150Ω, we can solve for XL:
200^2 = 150^2 + XL^2 => XL = √(200^2 - 150^2)
After calculating XL, we can find the frequency (f) by rearranging the formula for inductive reactance:
f = XL / (2πL)
We then substitute the calculated value of XL and the given L (50mH) to find the desired frequency.