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.