Consider a series RL circuit with R= 84.0 and an unknown inductor L, driven by a

Question

Consider a series RL circuit with R= 84.0 and an unknown inductor L, driven by an AC emf with Erms= 33.0 Volts at frequency f= 6.80 kHz. If we measure the current in the circuit, we find Irms= 0.167 Amps.

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= 84.0 and an unknown inductor L, driven by an AC emf with Erms= 33.0 Volts at frequency f= 6.80 kHz. If we measure the current in the circuit, we find Irms= 0.167 Amps.

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.)

Explanation / Answer

33=0.167(84+jx):33=14.028+jx*0.167:33-14.028=jx*0.167:18.972/0.167=j113.605=XL 113.605/(2*pi*6800)=0.00266=L a) 2.66 mH b) (33 angle 0 degrees)/(84+j113.605)=(0.234 angle 53.52 degrees) 0.234^2*84=4.584 W with inductor:33^2/84=12.964 W c) ratio---> 4.584/12.94=0.354

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