Question

The charger cord used to recharge a cell phone contains a transformer that reduces 240 V AC to 4 V AC. For each 1,025 turns in the input coil, how many turns are there in the output coil? (Round your answer to at least one decimal place.)

Answer 1

Let:

V_p is the primary voltage (voltage on the input coil of transformer);

V_s is the secondary voltage (voltage on the output coil of transformer);

n_p is the number of turns in the input coil;

n_s  is the number of turns in the output coil.

These values are related by identity

$$\frac{{{V}_{p}}}{{{V}_{s}}}=\frac{{{n}_{p}}}{{{n}_{s}}}$$

which is the basic formula for transformers. Substituting into this identity the known values V_p=240 V, V_s=4 V and n_p=1,025 we get the equation for n_s:

$$\frac{240}{4}=\frac{1025}{{{n}_{s}}}$$

Solving this equation we get

$${{n}_{s}}=\frac{4\cdot 1025}{240}\approx 17.1$$

Thus, there are 17.1 turns in the output coil of the transformer.