#### The inductance measurements in coils and the effect of iron core to inductance

**Possible Experiments**
- The measurement of self inductance of coils,
- Self inductance of coils with iron core

**Standard Equipment**
DC power supply, ampermeter, voltmeter, 12ohm resistor, 2 coils, 1 coil with iron core, function generator, connection cables. The coils have radii of 20 mm and their length is 14 cm...

**Technical Information **
The circuits with coils behave differently to DC and Ac signals. They show an impedence (Z) to AC current. A coil to which an AC potential is shown in the figure. From this circuit one can write: V_{AC}=V_{AB}+V_{BC} where V_{AC}= L dI/dt + R I where I is current, dI/dt is its change, L is the inductance and R is the resistance. The reaktans: X_{L}=wL is a function of the angular frequency given by w=2πf with frequency: f. On a circuit with inductance, the voltages across resistor and coils have 90^{o} phase difference but the current through the resistor has the same phase with the voltage. If V_{L} is the inductance voltage, and V_{R} is the resistor voltage, their vector sum gives: Z^{2}=I L^{2}w^{2} + R^{2} . If R is measured by a multimeter, and Z is obtained from I-V graph, one can easily calculate L. Note that the self inductance of the cylindrical coil is L_{0}=μ_{0} A N^{2}/L where N is the number of windings, A is cross section area, L is the length and μ_{0} = 4πx10^{-7} H/m is the magnetic permeability of air. If an iron core is inserted thrugh the centerline of the coil, the inductance increases to L=μL_{0} where μ is the magnetic permeability of iron.

The serial coil filters high frequencies (low pass filter). This property can be examined by applying signals with different frequencies from the function generator and measuring the ratio of input and output voltages.