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Current is the amount of charge that goes through that point for a period of time. If the circuit does not branch, the current has to be the same - otherwise you'll have an accumulation of charge somewhere over it.
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Question: How does the current flowing through the wire at point P compare with the current flowing at Q.
Answer: The current at point P is the same.
Why is the current in a wire the same before and after it goes through a resistor?
Khan academy had a good explanation of this. Think of the first electron accelerating through the circuit. High speed....then bam! Resister. It slows down. It gets through resister, then it speeds back up and completes a complete turn.
When it starts going through a new lap, it approaches the resistor and it slows down before traversing it because there is a bottleneck. The electrons in front of it have been slowed down, so it has to slow down as well.
The whole circuit has the same current for this reason. They all go as fast as the slowest electron.
