A three-phase cylindrical rotor synchronous generator has a synchronous reactance $X_{s}$ and a negligible armature resistance. The magnitude of per phase terminal voltage is $V_{A}$ the magnitude of per phase induced emf is $E_{A}.$ Considering the following two statements, $P$ and $Q,$

$P:$ For any three-phase balanced leading load connected across the terminals of this synchronous generator, $V_{A}$ is always more than $E_{A}.$

$Q:$ For any three-phase balanced lagging load connected across the terminals of this synchronous generator, $V_{A}$ is always less than $E_{A}.$

which of the following options is correct?

- $P$ is false and $Q$ is true
- $P$ is true and $Q$ is false
- $P$ is false and $Q$ is false
- $P$ is true and $Q$ is true