In Resnick halliday, student 10th edition page - 795. In the topic current decay in RL circuit, the following statement is used, the connection to b must actually be made an instant before the connection to a Is broken. Why is that actually required? Please refer to the attached diagram.
When you connect $S$ to $a$, the current will exponentially rise to its final value determined by $\varepsilon/R$. Please note that in a circuit with energy storage elements (inductors, capacitors, etc.) things do not happen instantaneously: current cannot change instantaneously in an inductor but voltage can, and vice-versa for capacitors.
Now imagine what happens when you disconnect $S$ and $a$ - since there was some current in the circuit prior to the "disconnecting event", the current cannot instantaneously drop to zero due to the inductor. If you do not connect it to $b$ immediately after disconnecting from $a$, the voltage across the inductor will reverse as large as needed to keep the current flowing. This will finally create an arc across the air gap (switch), and the current will keep flowing. Note that this is a real problem in engineering that can destroy the voltage source $\varepsilon$, which in most situations can be easily solved by using a freewheling diode which will limit the reverse voltage.
This situation is actually similar to a light switch: $S$ is the switch, $R$ is the filament resistance (light bulb), and $L$ is the wire inductance. When you turn off the light, you sometimes can see a blue light coming from the switch. This is an arc that happens within the switch for the same reason as explained above.
