A 9.0-V battery and switch are connected in series across...

A $9.0-\mathrm{V}$ battery and switch are connected in series across the primary coil of a transformer. The secondary coil is connected to a lightbulb that operates on $120 \mathrm{V}$. Draw the circuit. Describe in detail how you can get the bulb to light-not necessarily continuously.

Key Concepts

Transformer

A transformer is a device that uses two or more coils wound on a magnetic core to transfer electrical energy from one circuit to another through electromagnetic induction. The ratio of turns in the primary and secondary coils determines whether the voltage is stepped up or stepped down. This principle is fundamental in electrical engineering, allowing for voltage transformation without changing the input frequency.

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic field within a coil of wire induces a voltage, or electromotive force (EMF), in the coil. This is described mathematically by Faraday’s law, which states that the induced EMF is proportional to the rate of change of the magnetic flux. It is the core principle behind the operation of transformers and other devices like generators and inductors.

Switching Transients

Switching transients occur when a circuit containing inductive elements, such as a transformer’s primary winding, is abruptly switched on or off. Even though a battery produces direct current, the act of rapidly closing or opening a switch can create a brief, rapidly changing current. This change in current leads to a sudden variation in magnetic flux, and thus, a transient induced voltage in the secondary coil that can momentarily provide a high-voltage pulse.

Voltage Step-Up

Voltage step-up is the process of increasing an input voltage to a level that is higher on the output side using a transformer. The operation is based on the ratio of the number of windings in the primary and secondary coils. A higher number of turns in the secondary relative to the primary results in a proportionally higher voltage, which is crucial when a high voltage is needed to operate devices, despite a low voltage source.

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