ELECTRICAL MEASUREMENTS 175 



valuable complexities into the consideration of electricity. Any conductor 

 carrying a current is surrounded by a magnetic field. When the circuit 

 is broken this field collapses, only to expand again when the current 

 starts flowing. Any d-c conductor, then, is surrounded by a steady mag- 

 netic field which goes through transitory changes only when a switch is 

 opened or closed. The a-c conductor, however, is surrounded by a mag- 

 netic field which is continually expanding or collapsing. If this expand- 

 ing and contracting magnetic field moves through a second wire, a cur- 

 rent will be induced in this second wire. Now imagine a coil of wire 

 conducting an alternating current. The expanding magnetic field around 

 one turn of the coil cuts across the next turn in the coil, inducing a cur- 

 rent in this second turn of the coil in the opposite direction. The net 

 effect throughout the coil is an induced current of opposite sign, which 

 tends to impede the original current. Impedance from this source oc- 

 curs in addition to the regular resistance of the wire in the coil. Thus 

 in any treatment of an a-c circuit which contains such coils we must 

 consider the inductance as well as the resistance. 



Another device produces a more-or-less opposite effect. A capacitor 

 (condenser) consists of a pair of plates of conducting material separated 

 from each other by a dielectric (insulating) material. If the two plates 

 are connected by wires to a d-c circuit, no current will flow through the 

 dielectric material, but an excess of electrons accumulates in one of the 

 plates and a deficiency in the other. The capacitor becomes charged, one 

 plate positively, the other negatively. In an alternating circuit, electrons 

 pour freely into one plate, forcing electrons out of the other plate. When 

 the sign of the current is reversed, the events occur in the opposite di- 

 rection. The capacitor seems to conduct a-c. The current flows so freely 

 into the large plates of the capacitor, however, that the resistance seems 

 smaller than if the capacitor were not present. 



The inductive eff^ect of a coil and the capacitive eff^ect of the con- 

 denser become very important in any a-c circuit in which they occur. 

 Instead of ordinary resistance, we speak of impedance (Z), and 

 1 = E/Z. The inductance (L) of a coil (in henries) affects the current 

 in a manner which is dependent on the alternating frequency (f). The 

 opposition to the current is called inductive reactance, Xl = l^rfL. The 

 condenser of capacitance C (in farads) produces an opposite effect, so 

 capacitive reactance Xr = l/(27r/C). The impedance Z is the vectorial 

 sum of resistance R and the net reactance. 



Z = Jr^ + (27rfL - \/27TfCy 



