Parallel Circuits With Resistance and Capacitance

When two or more circuits with resistance and capacitance are connected in parallel to a common source of voltage, each circuit acts as if it existed alone. The total current drawn by all the circuits may be calculated by the same method as was used for inductive circuits in Example 5-5.

Series Circuits With Resistance, Inductance, and Capacitance. - The characteristics of series circuits with resistance, inductance, and capacitance may best be studied by solving an example.

Example 5-9. - As shown in Fig. 5-17, a resistor with resistance RR = 10 ohms, an inductive reactor with 60-cycle reactance XL = 50 ohms and resistance RL = § ohms, and a condenser with 60-cycle reactance Xc = 45 ohms are connected in series to a 60-cycle line of 220 volts. Find the current, the voltage across the inductive reactor, and the voltage across the condenser.

Fig. 5-17. Resistance, Inductance, and Capacitance in Series

Solution.

The voltage across the inductive reactor is The voltage across the condenser is The most important point to be noted in Example 5-9 is that, while the whole circuit has only 220 volts applied to it, the condenser part of the circuit suffers a potential of 625.5 volts. If the condenser were designed for only 220 volts, there would almost certainly be a puncture of its insulation. In general, an excessive voltage

of 697.7 volts applied to an inductance coil designed for only 220 volts would not endanger the coil unless it were the cause of excessive current which might cause overheating.

Fig 5-18 Vector Diagram for Example 5-9

If the capacitance or inductance of a series circuit be so adjusted that the voltage across the capacitor is just equal to the inductive voltage in the reactor at some frequency, the circuit will act as if neither inductance nor capacitance were present at that frequency and the resistance alone will limit the current. This condition is called series resonance. One practical use of series resonance is found in some types of radio receivers in which a feeble voltage change between the antenna and the ground is made to provide a relatively large voltage change for use on the grid of the first amplifying tube.