f R = 50 Ω and XL = 20 Ω, find ZT and θT.

To find the total impedance (ZT), we can use the formula for impedance in a series RLC circuit, which is ZT = sqrt(R^2 + XL^2).

Step 1: Substitute the given values into the formula. ZT = sqrt((50 Ω)^2 + (20 Ω)^2)

Step 2: Calculate the square of each value. ZT = sqrt((2500 Ω^2) + (400 Ω^2))

Step 3: Add the two values. ZT = sqrt(2900 Ω^2)

Step 4: Take the square root of the result. ZT = 53.85 Ω

To find the total phase angle (θT), we can use the formula θT = arctan(XL / R).

Step 1: Substitute the given values into the formula. θT = arctan(20 Ω / 50 Ω)

Step 2: Calculate the division. θT = arctan(0.4)

Step 3: Find the arctangent of the result. θT = 21.8 degrees

So, the total impedance ZT is 53.85 Ω and the total phase angle θT is 21.8 degrees.