Purpose: To demonstrate the magnetic field lines that surround a current carrying conductor and a solenoid.

LR Circuit at Constant w and Variable L

With the switch S closed, the circuit is a series LR circuit and the RMS current through the bulb is given by

          V             V
     I = --- = -------------------
          Z     sqrt{ R2 + w2L2 }
        

where V = 120 V and w = 120*pi Hz. The value of L is maximized when the reluctance of the flux path of the inductor is minimized, and vice versa. The value of I is thus minimum when the movable part of the iron core is in line with the rest of the core and vice versa. The brightness of the bulb increases with the power, P = I²R, dissipated in the bulb. The two equations are thus demonstrated by moving the iron core from the up and out position where the bulb is moderately bright to the down and in position where the bulb goes out.

LRC Circuit at Constant w, R, C and Variable L. Resonance.

With the switch S open, the circuit is a series LRC circuit. The current through the bulb is given by

          V                 V
     I = --- = ---------------------------
          Z     sqrt{ R2 + (wL - 1/wC)2 }
        

When wL = 1/wC then I = V/R and the current through the bulb is maximum. This is the resonance condition, w = 1/sqrt{ LC }, which we achieve through adjustment of the position of the iron slug in the flux path of the inductor. At both the up (or minimum L) and down (or maximum L) positions, Z is large and the bulb is dim, but we can move the slug to an intermediate position that achieves the resonance condition. Resonance is demonstrated by the bulb at full brilliance, clearly greater than the maximum brightness found when C was shorted.

A very simple and reliable demonstration, but beware of electrocution!

Reluctance

The apparatus also demonstrates the concepts of reluctance and the definition of L.

          φ              Magnetomotive force    M
     L = ---  and    φ = ------------------- = --- ;
          I                  Reluctance         r

           M                 l
     L = -----  where  r = ------
          r*I               µ*A


μ   = permability of iron slug
l   = length of iron slug
A   = cross section of iron slug
φ   = flux through iron slug
    = flux through coil
I   = RMS current in coil

References: