An ac source of emf delivers 5.0 mW of power at an ms current of 2.0 mA when it is connected to

step 1 All right, so we're told that the power is 5 millawatts. And the current for the source, RMS, is

An ac source of emf delivers 5.0 mW of power at an ms...

An ac source of emf delivers 5.0 mW of power at an ms current of $2.0 \mathrm{mA}$ when it is connected to the primary coil of a transformer. The ms voltage across the secondary coil is $20 \mathrm{V}$. (a) What are the voltage across the primary coil and the current through the secondary coil? (b) What is the ratio of secondary to primary turns for the transformer?

Key Concepts

Voltage and Turns Ratio Relationship

The ratio of the voltages across the primary and secondary coils of a transformer is directly proportional to the ratio of the number of turns in their respective windings. This turns ratio determines how the transformer steps up or steps down the voltage from the primary side to the secondary side, and inversely affects the current to conserve power.

Conservation of Energy in Transformers

In the ideal transformer model, the power delivered to the primary coil is assumed to equal the power extracted from the secondary coil, neglecting losses such as thermal and magnetic losses. This power balance (Pin = Pout) underpins the relationships between voltage and current in the primary and secondary circuits.

AC Power and RMS Values

In AC circuits, the root mean square (RMS) values of voltage and current are used because they represent the effective or equivalent DC values that would deliver the same power. RMS values are critical in power calculations and circuit analysis, especially when evaluating the performance of devices like transformers.

Transformer Operation

A transformer is an electrical device that transfers energy between two or more circuits through electromagnetic induction. It typically consists of primary and secondary coils wound around a magnetic core. The alternating current in the primary coil creates a varying magnetic field that induces a voltage in the secondary coil, enabling voltage conversion between circuits.

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