To determine the characteristics of a coil of wire a student

To determine the characteristics of a coil of wire. a student connects the coil to a 12.0V battery After waiting for the circuit to stabilize the student observes that the coil draws a current of 752mA from the battery I he student next connects the coil to a signal generator oscillating with a 22.2 V_mass 121 Hz/signal The student observes that the coil now draws a current Of 475m Determine the resistance and the of the coil

Solution

When Coil is connected to a DC battery ,Resistance of the coil is given by

R=V/I =12/0.752

R=15.96 ohms

When the coil is connected to AC supply ,the Impedance of the coil is given by

Z=V_rms/I_rms =22.2/0.475

Z=46.74 ohms

SInce

Z=sqrt[R²+X_L²]

So inductive reactance is

X_L=sqrt[46.74²-15.96²] =43.93 ohms

since X_L=2pifL

=>L=X_L/2pif =43.93/2pi*121

L=0.05778 H or 57.78 mH