Answer :
Final answer:
The phase difference between the voltage and current in the given RLC circuit is approximately 0.309 radians.
Explanation:
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:
- Φ is the phase difference
- ω is the angular frequency (2πf)
- L is the inductance
- C is the capacitance
- R is the resistance
Given values:
- R = 7.9 ohms
- L = 35.5 mH (convert to H: 35.5 × 10-3 H)
- C = 15.2 F
- Operating frequency = 46 Hz
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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