Self-induction causes the current to _lag_, that is, the current does not quite reach its maximum at the instant the voltage reaches its maximum. Fig. 434 shows graphically an e.m.f. and a lagging current. In this figure the maximum current is shown following the maximum voltage at an interval of 30 degrees. In other words the armature in a two-pole field must turn 30 degrees from the position of maximum voltage before the current in the coil, where the self-induction occurs, reaches its maximum. =434. Reactance and Impedance.=--A choke coil has resistance as well as inductance. Its resistance can be found by the voltmeter-ammeter method, using a direct current. (See Art. 278.) Let us take for example the primary winding of a bell ringing transformer. Using a direct current and testing the coil with a voltmeter and ammeter we find its resistance to be, let us say, one ohm. If we connect the same coil across a 110 volt a.-c. line we find the current to be very small, say 0.05 ampere. The coil now has resistance and _reactance_. Reactance is the effect of self-induction in hindering the flow of current. It is measured in ohms. The combined effect of resistance and reactance is called _impedance_. In the example above, the coil has 110 (volts)/0.05 (ampere) = 2200 ohms of impedance. In applying Ohm's law to an alternating current circuit, impedance must be substituted for resistance. Ohm's law as applied to an a-c. circuit should be stated: "Current intensity equals e.m.f. divided by impedance", or _I_ = _E_/_Z_. (_Z_ = impedance.) [Illustration: FIG. 435.--The relation between resistance, reactance and impedance.] Impedance, however, does not equal the _sum_ of resistance and reactance. The relation between these three quantities is similar to that between the three sides of a right triangle, in which the impedance represents the hypotenuse, and the resistance and reactance the other two sides. See Fig. 435 which indicates that Resistance² + Reactance² = Impedance², or (_R²_ + _X²_ = _Z²_). (_X_ = reactance.) To illustrate this relation; suppose the primary of a transformer has 10 ohms impedance and 8 ohms resistance, then the reactance equals 10² - 8² = 6², or the reactance is 6 ohms. Exercises 1. Find the reactance of a choke coil having a resistance of 10 ohms, when its impedance is 50 ohms. How great a current flows through this coil if the terminal voltage is 110 volts? 2. When the bell is ringing, the primary of a bell ringing transformer has an appreciable current. Suppose this current is 0.2 ampere. What is the impedance if the voltage of the line is 115 volts? What is the reactance if the resistance is 1 ohm? 3. The primary of a large transformer has a terminal voltage of 6000 volts and a current of 600 amperes. What is the impedance? If the resistance is 6 ohms, what is the reactance? [Illustration: FIG. 436.--A telephone set showing a condenser used in the circuit of the "ringer."]