In a parallel circuit, E_T = 208 V, R = 33 k Ω , and X_L = 82 k Ω . What is the apparent power?

A) 0.14 VA
B) 0.31 VA
C) 1.22 VA
D) 1.41 VA

The apparent power in a parallel circuit can be calculated using the formula $S=\frac{V^2}{Z}$ , where $S$ is the apparent power in volt-amperes (VA), $V$ is the voltage across the circuit, and $Z$ is the impedance of the circuit. The impedance $Z$ in a parallel circuit with resistance $R$ and inductive reactance $X_L$ can be found using the formula for the total impedance in a parallel R-L circuit: $\frac{1}{Z}=\sqrt{{\left(\frac{1}{R}\right)}^2+{\left(\frac{1}{X_L}\right)}^2}$ . Given $V=208$ V, $R=33$ kΩ, and $X_L=82$ kΩ, we first convert kΩ to Ω (1 kΩ = 1000 Ω), then calculate $Z$ , and finally calculate $S$ .First, convert kΩ to Ω:- $R=33$ kΩ = $33,000$ Ω- $X_L=82$ kΩ = $82,000$ ΩCalculate $Z$ :- $Z={\left(\sqrt{{\left(\frac{1}{R}\right)}^2+{\left(\frac{1}{X_L}\right)}^2}\right)}^{-1}$ - $Z={\left(\sqrt{{\left(\frac{1}{33,000}\right)}^2+{\left(\frac{1}{82,000}\right)}^2}\right)}^{-1}$ - $Z$ calculates to approximately $27,000$ Ω (rounded for simplification of explanation).Calculate $S$ :- $S=\frac{V^2}{Z}=\frac{208^2}{27,000}$ - $S$ calculates to approximately $1.6$ VA, which is not an option provided. However, it seems there was a mistake in the calculation explanation above. Let's correct the approach for calculating the apparent power correctly:The correct approach involves using the given values directly without the need for detailed impedance calculation since the apparent power formula provided initially was incorrect for a parallel circuit scenario. The correct method to find the apparent power in any AC circuit is by using the formula $S=\frac{V^2}{Z}$ , but with the understanding that $Z$ is the combined impedance of the circuit, which needs to be calculated correctly from the given resistance and reactance.Given the error in the calculation process described, let's simplify to the correct answer based on the options provided:The apparent power $S$ can be approximated in a parallel circuit by considering the voltage and the total impedance. Without the detailed impedance calculation provided in the initial explanation, the correct answer should be determined based on the understanding that apparent power in a parallel AC circuit involves both the resistance and reactance, but the detailed calculation provided initially led to an incorrect explanation path.Given the options and the typical calculation for apparent power in such circuits, the correct answer is intended to be derived from the voltage and impedance values in a manner that aligns with basic principles of electrical engineering. However, without the correct detailed calculation directly leading to one of the provided options, the selection of "D) 1.41 VA" was based on an incorrect explanation path. The correct calculation involves accurately determining the total impedance from the given resistance and reactance, then applying the voltage to find the apparent power, which was not correctly executed in the explanation.