RL Series Circuit... Help please!!?
Consider a series RL circuit with R= 63.0 Ω and an unknown inductor L, driven by an AC emf with Erms= 38.0 Volts at frequency f= 6.90 kHz. If we measure the current in the circuit, we find Irms= 0.185 Amps.
a. What is the inductance L?
b. What is the magnitude of the phase angle between the applied voltage and the current?
c. What is the ratio of the power dissipated in the resistor to the power that would be dissipated if the inductor were not in the circuit? (Assume that Erms stays the same.)
I already answered B.... Please help me to answer A and C with procedure because I havent been able to do it. Thank you!!!!
Comments
Capacitive Reactance Xc = 1/(2πfC)
Inductive Reactance Xʟ = 2πfL
Impedance Z = √(R² + X²)
where X = Xʟ – Xc
Phase angle θ = arctan (X/R)
Xc, Xʟ, Z are in Ω, f is in Hz
C in farads, L in Henrys
Given those numbers, the impedance is 38/0.185 = 205 ohms
Z = √(R² + X²) = 205
R² + X² = 42200
X² = 42200 – 63²
X = 196 ohms
Xʟ = 2πfL = 196
L = 0.00451 H or 4.51 mH
θ = arctan (X/R) = arctan (196/63) = 72.2º
Voltage across R is 0.185 x 43 = 8.0 volts
power = 8 x 0.185 = 1.47 watts
R alone, power is 38²/43 = 33.6 watts
(how could you do b without doing a first?)
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Series Rl Circuit