For this circuit which of the subsequent represents a correct way of connecting an ammeter to measure the current through resistor R2?

Answer:

An ammeter acts similar to a piece of wire that measures the charge flow rate through itself. To use it in principle one merely removes a piece of wire in that branch of the circuit through which one wishes to measure the current and replaces that piece of wire with the ammeter.

A branch of a circuit is as well known as a leg of a circuit. It is a solitary conducting path with no forks in the road. If the circuit consists of merely one single conducting path there is but one branch to the circuit the whole circuit is the one and only branch of the circuit. If the circuit has intersections where three or more wires meet then the circuit has more than one branch. Each single conducting path extending from one junction to another with no junctions in between is a branch of the circuit. The current all over in a branch of a circuit has one and the same value. To calculate the current through R2 in principle one has to remove a section of wire from the branch containing R2 and replace that section of wire with an ammeter. In practice this is the similar as disconnecting the wire from R2 connecting one end of the ammeter to the end of the wire just disconnected from R2 and the other end of the ammeter to the terminal of R2 from which the wire was removed.