What is the phase difference between the voltage and current in an RLC circuit with the following parameters?

- Resistance, R = 7.9 ohms
- Inductance, L = 35.5 mH
- Capacitance, C = 15.2 F
- Frequency = 46 Hz

(Answer in radians)

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Answer :

CoddyJones CoddyJones · Answer 1 · 2025-03-22T02:53:09-04:00

The phase difference between the voltage and current in the given RLC circuit is approximately 0.309 radians.

In an RLC circuit, the phase difference between the voltage and current can be calculated using the formula:

Φ = arctan((ωL - 1/(ωC))/R)

where:

Given values:

First, we need to calculate the angular frequency (ω) using the formula:

ω = 2πf

Substituting the given frequency:

ω = 2π × 46 Hz

Next, we can substitute the values into the phase difference formula:

Φ = arctan((ωL - 1/(ωC))/R)

Φ = arctan(((2π × 46 Hz) × (35.5 × 10-3 H) - 1/((2π × 46 Hz) × (15.2 F)))/7.9 ohms)

Calculating the expression inside the arctan function:

Φ = arctan(0.326)

Using a calculator, we find that the phase difference (Φ) is approximately 0.309 radians.

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