In a series RC circuit, ET = 240 V, R = 500 Ω, and XC = 500 Ω. What is the true power?
Group of answer choices

64.4 W

28.8 W

70.72 W

57.62 W

To calculate the true power (\(P_{\text{true}}\)) in a series RC circuit, we need to find the current first and then use that to determine the power dissipated in the resistor.

### Step 1: Calculate total impedance
The impedance in a series RC circuit is given by:
\[
Z = \sqrt{R^2 + X_C^2}
\]
Given:
- \(R = 500 \, \Omega\)
- \(X_C = 500 \, \Omega\)

\[
Z = \sqrt{500^2 + 500^2} = \sqrt{250000 + 250000} = \sqrt{500000} = 707.1 \, \Omega
\]

### Step 2: Calculate the current
The current \(I\) in the circuit is given by Ohm's Law:
\[
I = \frac{E_T}{Z}
\]
Where \(E_T = 240 \, V\).

\[
I = \frac{240}{707.1} = 0.339 \, \text{A}
\]

### Step 3: Calculate the true power
True power is the power dissipated by the resistor, which is calculated by:
\[
P_{\text{true}} = I^2 R
\]

\[
P_{\text{true}} = (0.339)^2 \times 500 = 0.1149 \times 500 = 57.45 \, W
\]

So the closest answer is approximately **57.62 W**.

### Answer: **57.62 W**

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the formula for calculating reactive power in an RC circuit?
2. How do we calculate the phase angle in a series RC circuit?
3. What is the difference between true power and apparent power?
4. How do capacitors affect the impedance in an AC circuit?
5. What happens to the current if the capacitance in the circuit increases?

**Tip:** In AC circuits, the true power is only dissipated by the resistive elements, while reactive components like capacitors and inductors store and release energy.

In a series RC circuit, ET = 240 V, R = 500 Ω, and XC = 500 Ω. What is the true power?

Discover how to calculate the true power in a series RC circuit with a supply voltage of 240V, resistance of 500Ω, and capacitive reactance of 500Ω. This detailed explanation includes step-by-step calculations using Ohm's Law and power formulas, ideal for students in Grades 11-12 or early electrical engineering studies.

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