The average power delivered to a series AC circuit is given by (symbols have their usual meaning):

Options

A. `E_(rms)I_(rms)`
B. `E_(rms)I_(rms) cos phi`
C. `E_(rms)I_(rms) sin phi`
D. zero

Answer

To solve the question regarding the average power delivered to a series AC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Average Power in AC Circuits**:
- In AC circuits, the average power (P) delivered to the circuit is not simply the product of voltage and current due to the phase difference between them. Instead, it is calculated using the root mean square (RMS) values of voltage and current.

2. **Define RMS Voltage and Current**:
- The RMS voltage (V_RMS) is the effective value of the alternating voltage, and the RMS current (I_RMS) is the effective value of the alternating current. These values are used because they provide a way to calculate power in AC circuits similarly to how we do in DC circuits.

3. **Introduce the Power Factor**:
- The power factor (cos φ) is defined as the cosine of the phase angle (φ) between the voltage and current waveforms. It accounts for the fact that not all the power supplied by the source is used for useful work due to this phase difference.

4. **Write the Formula for Average Power**:
- The average power (P) in a series AC circuit can be expressed with the formula:
\[ P = V_{RMS} \cdot I_{RMS} \cdot \cos φ \]
- Here, \(V_{RMS}\) is the RMS voltage, \(I_{RMS}\) is the RMS current, and \(\cos φ\) is the power factor.

5. **Relate EMF to Voltage**:
- In the context of the question, it is mentioned that E represents the electromotive force (EMF), which is equivalent to the RMS voltage (V). Therefore, we can replace \(V_{RMS}\) with E in our formula.

6. **Final Expression for Average Power**:
- Substituting E for \(V_{RMS}\) in the power formula gives us:
\[ P = E \cdot I_{RMS} \cdot \cos φ \]
- This is the final expression for the average power delivered to a series AC circuit.

### Conclusion:
The average power delivered to a series AC circuit is given by:
\[ P = E_{RMS} \cdot I_{RMS} \cdot \cos φ \]