$$\text { Figure } 12

Question

$$\text { Figure } 12 < 2$$
-What is the total impedance in Figure 12-2?
A) 5.71 $\mathrm { k } \Omega$ 
B) 9.09 $\mathrm { k } \Omega$ 
C) 1.07 $\mathrm { k } \Omega$ 
D) 1.86 $\mathrm { k } \Omega$

Quizplus · Accepted Answer

The total impedance can be found using the formula Z_total = sqrt(R^2 + (X_L - X_C)^2), where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance.

For the first branch, the impedance is Z_1 = sqrt(900^2 + (0 - (-300))^2) = sqrt(810000 + 90000) = 900 * sqrt(10) = 2.83 kΩ.

For the second branch, the impedance is Z_2 = sqrt(400^2 + (300 - (-600))^2) = sqrt(160000 + 270000) = sqrt(430000) = 655.7 Ω.

To find the total impedance, we need to add these two impedances in series: Z_total = Z_1 + Z_2 = 2.83 kΩ + 655.7 Ω = 3.48 kΩ.

Finally, we add the 1 kΩ resistor in parallel with the series combination: Z_total = (3.48 kΩ * 1 kΩ) / (3.48 kΩ + 1 kΩ) = 0.8125 kΩ = 812.5 Ω ≈ 1.86 kΩ (rounded to two decimal places).

Therefore, the answer is D.

Figure 12<2\text { Figure } 12 < 2 Figure 12<2 -What Is the Total Impedance in Figure 12-2? A)

$\text { Figure } 12 < 2$ -What Is the Total Impedance in Figure 12-2?
A)