Extract: ● I E(x, t)=-9.25. cos (105nt+ ·x+ 18 3 The phase velocity. The period of the wave. ● The wavelength. • The direction of propagation. ● The attenuation number.
Short Transmission Line
A short transmission line is a transmission line that has a length less than 80 kilometers, an operating voltage level of less than 20 kV, and zero capacitance effect.
Power Flow Analysis
Power flow analysis is a topic in power engineering. It is the flow of electric power in a system. The power flow analysis is preliminary used for the various components of Alternating Current (AC) power, such as the voltage, current, real power, reactive power, and voltage angles under given load conditions and is often known as a load flow study or load flow analysis.
Complex Form
A power system is defined as the connection or network of the various components that convert the non-electrical energy into the electric form and supply the electric form of energy from the source to the load. The power system is an important parameter in power engineering and the electrical engineering profession. The powers in the power system are primarily categorized into two types- active power and reactive power.
EMWAVE(NEED A NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE)
![### Wave Analysis
Consider the wave equation given by:
\[ \vec{E}(x, t) = -\hat{y} 9.25 \cos \left(10^5 \pi t + \frac{\pi}{18} x + \frac{\pi}{3} \right) \]
Let's extract some key properties of this wave:
- **The Phase Velocity:** The phase velocity \( v_p \) of the wave.
- **The Period of the Wave:** The period \( T \) of the wave.
- **The Wavelength:** The distance \( \lambda \) between successive peaks of the wave.
- **The Direction of Propagation:** The direction in which the wave is moving.
- **The Attenuation Number:** Any attenuation factor, if present, that signifies how the wave diminishes in amplitude over distance or time.
### Analysis
1. **The Phase Velocity ( \( v_p \) ):**
Phase velocity \( v_p \) is given by \( v_p = \frac{\omega}{k} \), where \( \omega \) is the angular frequency and \( k \) is the wave number.
2. **The Period of the Wave ( \( T \) ):**
The period can be derived from the angular frequency \( \omega \) using \( T = \frac{2\pi}{\omega} \).
3. **The Wavelength ( \( \lambda \) ):**
The wavelength can be found using the wave number \( k \) with the relation \( \lambda = \frac{2\pi}{k} \).
4. **The Direction of Propagation:**
The wave propagates in a direction determined by the sign and coefficients of \( x \) and \( t \) in the cosine argument.
5. **The Attenuation Number:**
The wave equation presents no exponential decay factors, so there is no attenuation implied in the provided equation.
### Detailed Derivation
1. **Finding \( k \) and \( \omega \):**
From the given wave equation:
\[ \vec{E}(x, t) = -\hat{y} 9.25 \cos \left(10^5 \pi t + \frac{\pi}{18} x + \frac{\pi}{3} \right) \]
- \( \omega = 10^5 \pi \)
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