Why do you think it is essential to measure current in a series circuit instead of in a parallel circuit?
What would happen if you simply connected the current probe to opposite sides of the resistor?
Ammeter measures value of current flowing in circuit, so current should flow inside ammeter to give proper result. And it has very low resistance to ensure the correct measurement of current in the circuit.
If it is connected in parallel across any load then all current in circuit will choose lower resistive path (i.e ammeter) to cause it's circuit to be damaged. Hence it is used in series.
When connected on the opposite sides of the resistor, only the sign of the current value will change.
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