Circuit Theory/Shorted Resistors
A wire in the left circuit is shorting the 100Ω resistor. All current will bypass the resistor and travel through the short. The voltage across the 100Ω resistor is going to be zero. The 100Ω resistor is not impacting the circuit. For analysis purposes, the 100Ω resistor can be removed.
The real world wire is going to have some resistance, and a tiny trickle of current will go through the resistor. The exact magnitude is going to depend upon the amount of resistance in the wire. The ideal math would involve infinity. So typically the assumption of a short is done by redrawing the circuit. This is why redrawing circuits when making assumptions (such as removing a resistor because of the short) is important.