Can you give me a similar question and solve it step by step please.A series RLC circuit has a resistance of 15 ⌦ and an impedance of 30 ⌦. What average power is delivered to this circuit when Vrms = 150 V?

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**Similar Question:**
A series RLC circuit has a resistance of 20 Ω and an impedance of 40 Ω. What average power is delivered to this circuit when Vrms = 200 V?

### Step-by-Step Solution

1. **Identify the Given Values:**
   - Resistance \( R = 20 \, \Omega \)
   - Impedance \( Z = 40 \, \Omega \)
   - RMS Voltage \( V_{rms} = 200 \, V \)

2. **Calculate the Current:**
   The RMS current \( I_{rms} \) can be calculated using the formula:
   \[
   I_{rms} = \frac{V_{rms}}{Z}
   \]
   Substituting the values:
   \[
   I_{rms} = \frac{200 \, V}{40 \, \Omega} = 5 \, A
   \]

3. **Calculate the Power Factor:**
   The power factor \( \cos(\phi) \) can be found using the formula:
   \[
   \cos(\phi) = \frac{R}{Z}
   \]
   Substituting the values:
   \[
   \cos(\phi) = \frac{20 \, \Omega}{40 \, \Omega} = 0.5
   \]

4. **Calculate the Average Power:**
   The average power \( P \) delivered to the circuit is given by:
   \[
   P = V_{rms} \cdot I_{rms} \cdot \cos(\phi)
   \]
   Substituting the known values:
   \[
   P = 200 \, V \cdot 5 \, A \cdot 0.5 = 500 \, W
   \]

### Final Answer:
The average power delivered to the circuit is **500 W**.

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Would you like more details on any of these steps, or do you have any questions? Here are some related questions to explore further:

1. How would the average power change if the impedance increased while keeping the RMS voltage constant?
2. What is the significance of the power factor in AC circuits?
3. How do you calculate the total reactance in an RLC circuit?
4. What would happen to the power delivered if the resistance were doubled?
5. How can you find the resonant frequency in an RLC circuit? 

**Tip:** Remember to always check your units when performing calculations to avoid errors!

A series RLC circuit has a resistance of 15 ⌦ and an impedance of 30 ⌦. What average power is delivered to this circuit when Vrms = 150 V?

Explore how to calculate the average power in a series RLC circuit with a resistance of 15 Ω and an impedance of 30 Ω when the RMS voltage is 150 V. This detailed guide includes all necessary formulas and step-by-step explanations, ideal for students in Grades 11-12.

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