1 Answer
The difference between true power and apparent power lies in how they relate to the energy consumed and the energy that is available in an AC (alternating current) electrical system. Here’s a breakdown of each:
1. True Power (P):
P = V \times I \times \cos(\theta)
\]
where:
- \( V \) is the voltage,
- \( I \) is the current,
- \( \theta \) is the phase angle between the voltage and current (also related to the power factor).
2. Apparent Power (S):
S = V \times I
\]
Relationship Between True Power, Apparent Power, and Reactive Power:
The relationship between true power (P), apparent power (S), and reactive power (Q) (which causes no work) can be summarized using the power triangle:
\[
S^2 = P^2 + Q^2
\]
Where:
Key Differences:
| Aspect | True Power (P) | Apparent Power (S) |
|----------------------|-------------------------------------|-------------------------------------|
| Measured In | Watts (W) | Volt-amperes (VA) |
| Definition | Power that performs useful work | Total power supplied to the circuit |
| Formula | \( P = V \times I \times \cos(\theta) \) | \( S = V \times I \) |
| Relation to Circuit | Used in performing work (e.g., lighting, heating) | Includes both useful power and reactive power |
Key Takeaways:
The power factor (\( \cos(\theta) \)) is a measure of how efficiently apparent power is being converted into true power.
1. True Power (P):
- Definition: True power, also known as active power, is the actual power that is consumed by the electrical load (like a motor, light bulb, or heating element) to perform useful work.
- Unit: It is measured in watts (W).
- Formula:
P = V \times I \times \cos(\theta)
\]
where:
- \( V \) is the voltage,
- \( I \) is the current,
- \( \theta \) is the phase angle between the voltage and current (also related to the power factor).
- Significance: This is the power that is actually used in a circuit, for example, to light a bulb or heat an element.
2. Apparent Power (S):
- Definition: Apparent power is the total power that flows from the source to the load. It combines both true power and reactive power (which does no useful work).
- Unit: It is measured in volt-amperes (VA).
- Formula:
S = V \times I
\]
- Significance: Apparent power represents the total power "appearing" to be supplied to the circuit, but it includes both useful power and power that doesn’t do any real work (reactive power).
Relationship Between True Power, Apparent Power, and Reactive Power:
The relationship between true power (P), apparent power (S), and reactive power (Q) (which causes no work) can be summarized using the power triangle:
\[
S^2 = P^2 + Q^2
\]
Where:
- \( P \) is the true power (measured in watts),
- \( Q \) is the reactive power (measured in volt-amperes reactive, or VAR),
- \( S \) is the apparent power (measured in volt-amperes, or VA).
Key Differences:
| Aspect | True Power (P) | Apparent Power (S) |
|----------------------|-------------------------------------|-------------------------------------|
| Measured In | Watts (W) | Volt-amperes (VA) |
| Definition | Power that performs useful work | Total power supplied to the circuit |
| Formula | \( P = V \times I \times \cos(\theta) \) | \( S = V \times I \) |
| Relation to Circuit | Used in performing work (e.g., lighting, heating) | Includes both useful power and reactive power |
Key Takeaways:
- True Power is the "real" power that does useful work.
- Apparent Power is the total power that’s available in the circuit, but it includes both the power that performs work and the power that does not (reactive power).
The power factor (\( \cos(\theta) \)) is a measure of how efficiently apparent power is being converted into true power.