Explanation:

When all three phases of a power system are short-circuited, it results in a symmetrical fault current. Let's understand why this happens:

1. Definition of a Symmetrical Fault:
A symmetrical fault, also known as a balanced fault or three-phase fault, occurs when all three phases of a power system are short-circuited together. In this case, the fault impedance is considered to be zero, and the fault is assumed to be symmetrical with respect to all three phases.

2. Phases in a Power System:
A power system typically consists of three phases - Phase A, Phase B, and Phase C. Each phase carries a sinusoidal voltage waveform that is 120 degrees out of phase with respect to the other phases. These three phases are responsible for supplying power to the electrical loads.

3. Short Circuit:
A short circuit occurs when a fault develops in the power system, causing an unintended connection between two or more conductors. It leads to a sudden increase in current flow, which can be potentially dangerous and damaging to the equipment.

4. Symmetrical Fault Current:
When all three phases of a power system are short-circuited together, the fault current that flows is symmetrical in nature. This means that the fault current waveform in each phase is identical and in phase with each other.

5. Implication of Symmetrical Fault Current:
The symmetrical fault current has several implications in power system analysis and protection:

- Calculations: It simplifies the calculations and analysis of fault current magnitudes and fault clearing times.
- Fault Detection: The symmetrical nature of the fault current helps in the detection and localization of faults in the power system.
- Protection Devices: Protection devices such as circuit breakers and relays are designed to respond to symmetrical fault currents and isolate the faulty section from the rest of the system.

Conclusion:
When all three phases of a power system are short-circuited, it results in a symmetrical fault current. This fault current is characterized by identical waveforms and magnitudes in each phase, simplifying fault analysis and aiding in the protection and detection of faults in the power system.