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Home Circuits With Resistance, Inductance, and Capacitance MultiPart Series Circuit with Resistance and Inductance  
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MultiPart Series Circuit with Resistance and InductanceAuthor: E.E. Kimberly When two or more devices with resistance and inductance are connected in series across an alternating voltage, the resistance of the whole is the arithmetical sum of the resistances of all the parts and the inductance of the whole is the arithmetical sum of the inductances of all the parts. Example 54.  A coil having resistance R_{1} = 20 ohms and inductance L_{1} = 0.10 henry is connected in series with a second coil having resistance R_{2} = 50 ohms and inductance L_{2} = 0.05 henry. It is required to force 10 amperes with 60cycle frequency through this circuit. What must be the applied voltage? Solution.  The schematic circuit diagram is shown in Fig. 59. The total resistance is
Also, the total inductance is
The remainder of the solution follows:
Voltmeter Vi, Fig. 59, measures the voltage I(R_{1}+jX_{1}) across the impedance R_{1}+jX_{1}. Voltmeter V_{2} measures the voltage I(R_{2}+jXz) across the impedance R_{2}+jX_{2} The readings of these voltmeters may be computed as follows:
I The arithmetical sum of Vi and Vz is greater than 900, the required voltage, but this sum has no significance because Vi and Vz are not in phase. Their vector sum is 900. The impedance diagram is shown in Fig. 510.


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