Question

A transformer has a primary coil with 400 turns of wire and a secondary coil with 1,600 turns. An AC generator connected across the primary coil has a voltage given by the function Δv = (180 V)sin(t).

What rms voltage (in V) is measured across the secondary coil?

Answer 1

The voltage across the secondary coil is related to the voltage across the primary coil by the turns ratio of the transformer. The turns ratio is defined as the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. In this case, the turns ratio is 1600 turns / 400 turns = 4.

The rms voltage across the secondary coil is given by the following formula:

V_secondary_rms = V_primary_rms * turns ratio

where V_primary_rms is the rms voltage across the primary coil.

The rms voltage across the primary coil is given by the following formula:

V_primary_rms = Δv / (2^0.5) = Δv / 1.41

where Δv is the peak voltage of the AC generator.

Substituting Δv = 180 V and evaluating the above formula, we get:

V_primary_rms = 180 V / 1.41 = 127.46 V

Substituting the value of V_primary_rms into the equation for the secondary coil, we get:

V_secondary_rms = 127.46 V * 4 = 509.84 V

So, the rms voltage measured across the secondary coil is 509.84 V.