To find the phase angle between the current and the voltage, we can use the formula:
tan(φ) = (wL - 1/wC) / R
Where:
φ = phase angle
w = angular frequency = 2πf
L = inductance
C = capacitance
R = resistance
In this case, there is no capacitor in the circuit, so wC = 0. Thus, the formula simplifies to:
tan(φ) = wL / R
Given:
f = 120 Hz
w = 2πf = 2π(120) = 240π rad/s
L = 0.5 H
R = 220.0 Ω
Plugging in these values, we get:
tan(φ) = (240π)(0.5) / 220.0
Using a calculator, we find:
tan(φ) ≈ 3.456
To find the phase angle φ, we take the arctan of 3.456:
φ ≈ arctan(3.456)
Using a calculator, we find:
φ ≈ 68.38°
Therefore, the correct answer is B. 68.38°.