Answer:
True
Step-by-step explanation:
Charge is conserved. If, along a wire, the current at one point was bigger than the current at a later point, that would imply charge is building up somewhere in between the two points. That would eventually (quickly) cause the wire to explode, and the wires aren’t exploding. So, charge isn’t building up, and this means along a single piece of wire the current is always the same.
If there is a junction in the wire, where the wire splits into two, then the current incoming equals the current outgoing, for the same reason that charge can’t build up at the junction. So, if current coming in is i1 , and in the two outgoing wires the currents out are i2 and i3, then current conservation implies
i1=i2+i3
In fact, by changing the definitions of the currents so that incoming current is positive on each wire, and outgoing current is negative on each wire, we can write the current conservation equation for a general junction with n wires as
0=∑nk=1ik