An LVDT is supplied with a sinusoidal voltage of amplitude 5 V and fr...
At both sides of origin, voltages at the displacement of 1 mm would be the same.
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An LVDT is supplied with a sinusoidal voltage of amplitude 5 V and fr...
LVDT (Linear Variable Differential Transformer)
Given Data:
- Amplitude of sinusoidal voltage: 5 V
- Frequency of sinusoidal voltage: 1 kHz
- Reading of voltmeter for 1 mm displacement from null position: 1 V
To Determine:
- Reading of voltmeter for 1 mm displacement in the opposite direction from null position
Explanation:
Working Principle of LVDT:
- LVDT is a type of electromechanical transducer that converts linear displacement into an electrical signal.
- It consists of a primary coil, two secondary coils, and a movable core.
- The primary coil is connected to a sinusoidal voltage source, and the two secondary coils are connected in series opposition.
- When there is no displacement, the magnetic flux is equal in both secondary coils, resulting in zero output voltage.
- When the core is displaced in one direction, the magnetic flux in one secondary coil increases while the flux in the other coil decreases, resulting in a differential output voltage.
- The magnitude of the output voltage depends on the amplitude and frequency of the input voltage as well as the displacement.
Relationship between Output Voltage and Displacement:
- The output voltage of an LVDT is given by the equation Vout = K * V * d, where Vout is the output voltage, V is the voltage amplitude, K is the sensitivity constant, and d is the displacement.
- The sensitivity constant (K) represents the change in output voltage per unit displacement.
- In this case, the sensitivity constant is given as 1 V/mm.
Calculation:
- Given that the reading of the voltmeter for a displacement of 1 mm from the null position is 1 V.
- Using the equation Vout = K * V * d, we can calculate the sensitivity constant:
- 1 V = K * 5 V * 1 mm
- K = 1/5 V/mm = 0.2 V/mm
Reading of Voltmeter for 1 mm Displacement in the Opposite Direction:
- When the displacement is 1 mm in the opposite direction from the null position, the output voltage can be calculated using the equation Vout = K * V * d:
- Vout = 0.2 V/mm * 5 V * (-1 mm) = -1 V
Conclusion:
- The reading of the voltmeter for a displacement of 1 mm in the opposite direction from the null position is -1 V.
- Therefore, the correct answer is option C) 1 V.