AC Network Analysis

This phase-shifting bridge circuit is supposed to provide an output voltage with a variable phase shift from -45^o (lagging) to 45^o (leading), depending on the position of the potentiometer wiper:

Suppose, though, that there is a solder “bridge” between the terminals of resistor R₁ on the circuit board. What effect will this fault have on the output of the circuit? Be as complete as you can in your answer.

This phase-shifting bridge circuit is supposed to provide an output voltage with a variable phase shift from -45^o (lagging) to 45^o (leading), depending on the position of the potentiometer wiper:

Suppose, though, that the output signal is stuck at 45^o leading the source voltage, no matter where the potentiometer is set. Identify a likely failure that could cause this to happen, and explain why this failure could account for the circuit’s strange behavior.

This phase-shifting bridge circuit is supposed to provide an output voltage with a variable phase shift from -45^o (lagging) to 45^o (leading), depending on the position of the potentiometer wiper:

Suppose, though, that the output signal registers as it should with the potentiometer wiper fully to the right, but diminishes greatly in amplitude as the wiper is moved to the left, until there is practically zero output voltage at the full-left position. Identify a likely failure that could cause this to happen, and explain why this failure could account for the circuit’s strange behavior.