# A synchronous motor operates at rated voltage and frequency and has a load torque angle of 30°. If both the terminal voltage and frequency are reduced

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A synchronous motor operates at rated voltage and frequency and has a load torque angle of 30°. If both the terminal voltage and frequency are reduced by 10%, then
1. the load torque angle remains the same
2. the load torque angle increases
3. the load torque angle decreases
4. nothing can be said about the torque angle

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Correct Answer - Option 1 : the load torque angle remains the same

Concept:

The power in a synchronous motor is given by,

$P = \frac{{EV}}{{{X_s}}}\sin \delta$

$P \propto \left( {\frac{{{V^2}}}{f}} \right)\sin \delta$

$T = \frac{P}{{{\omega _0}}};\;\;T \propto \left( {\frac{{{V^2}}}{{{f^2}}}} \right)\sin \delta$

Application:

The terminal voltage and frequency are reduced by 10% i.e. V/f ratio is constant and the torque angle δ is constant.

Therefore, the load torque remains the same.