A transformer connected to a 240$V_{r.m.s}$ has 3000 turns in its primary coil and 500 turns in its secondary coil. Calculate the output voltage.

Analyze the question: This is an ideal transformer problem. We're given the input (primary) voltage and the number of turns in each coil, and we need the output (secondary) voltage.

Concept: For a transformer, the voltage ratio equals the turns ratio:

where

• V_p = primary voltage = 240 V
• V_s = secondary voltage (what we want)
• N_p = primary turns = 3000
• N_s = secondary turns = 500

Solution:

Since the secondary has fewer turns than the primary, this is a step-down transformer, so the output voltage is smaller than 240 V. That agrees with our answer of 40 V.

Answer: The output voltage is 40 V (r.m.s.), which is option C.

Tip: Always check the direction. If N_s < N_p, the voltage steps down. If N_s > N_p, it steps up. This lets you quickly eliminate options like A (4000 V) and B (400 V), which are larger than the input. Also, simplify the turns ratio first (500/3000 = 1/6) to make the arithmetic easy without a calculator.