What is the inductance L? What is the magnitude of the phase angle between the a

Question

What is the inductance L?

What is the magnitude of the phase angle between the applied voltage and the current?

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.)

Consider a series RL circuit with R= 86.0 ? and an unknown inductor L, driven by an AC emf with Erms= 34.0 Volts at frequency f= 7.70 kHz. If we measure the current in the circuit, we find Irms= 0.137 Amps. Consider a series RL circuit with R= 86.0 ? and an unknown inductor L, driven by an AC emf with Erms= 34.0 Volts at frequency f= 7.70 kHz. If we measure the current in the circuit, we find Irms= 0.137 Amps. What is the inductance L? The impedance of the resistor and inductor in series must equal the voltage divided by the current. What is the magnitude of the phase angle between the applied voltage and the current? 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.)

Explanation / Answer

impedence Z= Vrms/irms = 34/0.137 = 248.175 ohms

but Z^2 also = R^2+ XL^2

so XL^2 = 248.175^2 -86^2

XL= 2pif L    = 232.79

thus L = 232.79/(2*3.14*7700) = 4.8 mH

b. phase angle cos theta = R/Z = 86/248.175 = 0.346

theta = 69.72 deg

c. power across resistor = i^2R = 0.137*0.137 * 86 = 1.614 Watts

power across inductor = i^2XL = 0.137*0.137 * 232.79 = 4.369 Watts

ratio is 1.614/4.369 = 0.369 or 36.9 %

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