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Concise Physics mentions that:

On connecting one more appliance in the same circuit , the resistance of the circuit will increase . Hence , it will reduce the current in the circuit , so each appliance will get less power .

www.allaboutcircuits.com mentions that;

The amount of current in a series circuit is the same through any component in the circuit. This is because there is only one path for current flow in a series circuit.

If the current in the series circuit should remain the same then how does current decreases in a series circuit of the resistance is increased? Why the voltage does not decrease in this case?

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The amount of current in a series circuit is the same through any component in the circuit. This is because there is only one path for current flow in a series circuit.

This means that at any point along a series circuit, the current is the same. The current is still free to change, but if it changes, it changes everywhere. This just means that whatever the current may be, you will measure the same current at any point along a series circuit.

As for why adding resistance decreases current, you can apply Ohm's Law. For the same potential difference, you get $I=\dfrac VR$ so as $R$ increases, $I$ decreases.

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