**Power Parallel Circuit**

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In steppingstone fashion, the discussion of series DC circuits will now be followed by a consideration of the characteristics of parallel DC circuits. It will be shown how the principles applied to series circuits can be used to determine the reactions of such quantities as voltage, current, and resistance in parallel circuits. Problems involving the determination of resistance, voltage, current, and power in a parallel circuit are solved as simply as in a series circuit. The procedure is the same 3.166), the recovery voltage of the parallel circuit shown is the sum of the power frequency voltage and the voltage across the inductance, therefore, e' = E sin(waf + <fl) — E sin 0 exp(— Rt/L) where, in addition to the other terms,.X hence de wnR — dt wnR /wnRr\ cos(w,r + 0) + E sin 0 expl I (3.32) X \ X i For purposes of comparison, the recovery voltage of the capacitive circuit (Fig. 3.14a) has a sinusoidal wave shape, hence the differential eq. 3.28 with respect to time is de' — = W The total power (PT) is then obtained by summing up the power dissipated in the branch resistors using equation 13.22. Because, in the example shown in figure 13.28, the total current is known, we could determine the total power by the following method: PT = Eb x IT PT = 50 v x 8a PT = 400 watts Rules for Solving Parallel DC Circuits Problems involving the determination of resistance, voltage, current, and power in a parallel circuit are solved as simply as in a series.circuit.circuit to tune the load circuit near resonance, the circuit impedance rises and the amount of current drawn from the power source falls off dramatically. The circuit voltage required to achieve a specific power level is the same as with the initial case of zero capacitance, but now the higher current required by the load is being supplied by the capacitors rather than the power source. In a paralleltuned load circuit we have a Q rise in current in the tank circuit compared with the input line Also, you can use: 1 1 1 Total power supplied to, or dissipated by, a parallel circuit is found with the power formulas PT = VT x IT, IT x RT, or VT2/RT, or by summing the power dissipations of all the branches. Power dissipated by.any branch of a parallel circuit is computed with the power formulas by substituting the specified branch V, I, and/or R parameters into the formulas, as appropriate. Branch power dissipations are such that the highest R value branch dissipates the least power, Andrei Grebennikov, Nathan O. Sokal, Marc J Franco. 6.4 ParallelCircuit Class E The theoretical analysis of a switchedmode parallelcircuit ClassE power amplifier using a series filter with the calculation of the voltage and current waveforms and some graphical results was done by V. B. Kozyrev [17, 18]. Let us analyze the parallelcircuit ClassE mode in more detail. The basic circuit of a switchedmode parallelcircuit ClassE power amplifier is shown in Fig. 6.9(a). The load network EXAMPLE.11.42 Problem: What is the equivalent resistance of a 20ohm and a 30ohm resistor connected in parallel? Solution: Given: R1 = 20 ohms R2 = 30 ohms R RR =× × 12 2030 RR + = + = 12 2030 12ohms T 11.7.7.8 Power in Parallel Circuits As in the series circuit, the total power consumed in a parallel circuit is equal to the sum of the power consumed in the individual resistors. Note: Because power dissipation in resistors consists of a heat loss, power dissipations are Consequently, the simplified ratio between the operating power gain GP(E) of a parallelcircuit ClassE power amplifier and the operating power gain GP(B) of a conventional ClassB power amplifier with conjugatematched load can be written as GPðEÞ GPðBÞ 5.1 11 ðB22 1BÞ2R2ðEÞ RðEÞ RðBÞ (6.130) where R(E) is the load resistance of a ClassE power amplifier and R(B) is the load resistance of a ClassB power amplifier. For a nominal parallelcircuit ClassE operation mode R 2 30 ohms R 1 20 ohms E b + – + – (A) Original circuit 12 ohms (B) Equivalent circuit FIGURE 10.57 Parallel circuit with equivalent circuit. R eq This process is called reduction to an equivalent circuit. An example of circuit reduction was demonstrated in Example 10.28 and is illustrated in Figure 10.57. The circuit shown in Figure 10.57A is reduced to the simple circuit shown in Figure 10.57B. 10.17.9 poWer in parallel CirCUits As in the series circuit, the total power consumed in a POWER AND POWER FACTOR.The apparent power, true power, and reactive power in the parallel circuit are related as the hypotenuse, base, and altitude, respectively, ofa right triangle in a similar manner to that described in the preceding chapter. The relation between apparent power, true power, and reactive power is shown in figure 132 (E). The hypotenuse of the right triangle represents the apparent power and is equal to ER, or 100 x 7.07 = 707 voltamperes. The base of the