What will happen if potential divider was open circuited?

If a potential divider is open circuited, it essentially breaks the circuit, preventing any current from flowing through it. As a result, the output voltage across the divider will become undefined, as there is no current to develop a voltage drop across the resistors. This means that the intended voltage division will not occur, and the circuit will not function as designed. In practical terms, the output voltage may float to a value determined by any stray capacitance or noise, but it will not provide a stable or usable voltage.