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The inductor does not allow ac signal to pass through. It blocks ac and passes dc. If the switch is open, then the ac signal wont pass. If the switch is closed, then the ac signal will pass through the switch.

Answer

It is incorrect to say that an inductor 'does not allow' the passage of an alternating current. An a.c. current will pass through an inductor, although the inductor will limit the value of that current due to the inductor's inductive reactance. Inductive reactance, which is expressed in ohms, is directly-proportional to the inductance of the inductor and to the frequency of the supply. The value of the current is determined by dividing the supply voltage by the inductive reactance of the inductor.

If the switch is connected in parallel with the inductor, then closing the switch will apply a direct short circuit across the inductor, and the resulting short-circuit current will cause the circuit's protective device (fuse or circuit breaker) to operate.

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