Question

В цепи переменного тока резистор R=3 ом и конденсатор сопротивлением Xc= 4 ом соединены последовательно . Напряжение на резисторе равно Ur=20B. Определить полное сопротивление цепи, силу тока, активную и реактивную мощности

Answer 1

Вроде как-то так

Z=$\sqrt{R^2+(X_{L}-X_{C})^2}$
$\X_{L}=0$
Z=$\sqrt{R^2+(-X_{C})^2}$
Z=$\sqrt{9+16}$=5 Ом (полное сопротивление)
$I_{0}= U_{R}/R$=20/3=6,66 A (сила тока)
$P_{R}=UIcos$Ф=20*6,66*0,6/2=39,96 Вт (активная мощность)
$P_{R}=UIsin$Ф=20*6,66*0,8/2=53,28 Вт (реактивная мощность)

Answer 2

Calculation of Total Resistance (Rt):

To determine the total resistance (Rt) of the circuit, we need to add the resistance of the resistor (R) and the reactance of the capacitor (Xc) since they are connected in series.

The resistance of the resistor (R) is given as R = 3 Ω.

The reactance of the capacitor (Xc) is given as Xc = 4 Ω.

Since the resistor and the capacitor are connected in series, we can add their resistances to find the total resistance (Rt):

Rt = R + Xc = 3 Ω + 4 Ω = 7 Ω

Therefore, the total resistance (Rt) of the circuit is 7 Ω.

Calculation of Current (I):

To calculate the current (I) flowing through the circuit, we can use Ohm's Law, which states that the current is equal to the voltage divided by the resistance.

The voltage across the resistor (Ur) is given as Ur = 20 V.

Using Ohm's Law, we can calculate the current (I):

I = Ur / Rt = 20 V / 7 Ω ≈ 2.857 A

Therefore, the current (I) flowing through the circuit is approximately 2.857 A.

Calculation of Active Power (P) and Reactive Power (Q):

To calculate the active power (P) and reactive power (Q) in the circuit, we need to use the formulas:

P = I^2 * Rt (active power) Q = I^2 * Xc (reactive power)

Substituting the values we have:

P = (2.857 A)^2 * 7 Ω ≈ 57.959 W Q = (2.857 A)^2 * 4 Ω ≈ 32.653 VAR

Therefore, the active power (P) in the circuit is approximately 57.959 W and the reactive power (Q) is approximately 32.653 VAR.

Note: VAR stands for Volt-Ampere Reactive, which is the unit of reactive power.

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