47. A circuit consists of a 220.0Ω

resistor and a 0.5II inductor
connected across a generator that
has a frequency of 120Hz and a
voltage if 230V. Determine the
phase angle between the current
and the voltage
A. 59.73°
B. 68.38°
C. 26.75°
D. 30.27°
E. 38.21°

1 answer

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°.