Multi-Part Series Circuit with Resistance and Inductance

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 5-4. - A coil having resistance R₁ = 20 ohms and inductance L₁ = 0.10 henry is connected in series with a second coil having resistance R₂ = 50 ohms and inductance L₂ = 0.05 henry. It is required to force 10 amperes with 60-cycle frequency through this circuit. What must be the applied voltage?

Solution. - The schematic circuit diagram is shown in Fig. 5-9. The total resistance is

Fig. 5-9. Impedance Coils in Series

Also, the total inductance is

The remainder of the solution follows:

Voltmeter Vi, Fig. 5-9, measures the voltage I(R₁+jX₁) across the impedance R₁+jX₁. Voltmeter V₂ measures the voltage I(R₂+jXz) across the impedance R₂+jX₂ The readings of these voltmeters may be computed as follows:

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. 5-10.

Fig. 5-10. Impedance Diagram for Example 5-4