Question

The primary coil of a transformer has 250 turns; the secondary coil has 1000 turns. An alternating current is sent through the primary coil. The emf in the primary is of amplitude \(16 \mathrm{V}\). What is the emf amplitude in the secondary? (tutorial: transformer)

Short answer

Answer: 64V

Step-by-step solution

Identify the transformer equation.

The transformer equation is given by: \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\) where \(V_p\) is the emf amplitude in the primary coil, \(V_s\) is the emf amplitude in the secondary coil, \(N_p\) is the number of turns in the primary coil, and \(N_s\) is the number of turns in the secondary coil.

Plug in the given values.

We are given \(N_p = 250\) turns, \(N_s = 1000\) turns, and \(V_p = 16 \mathrm{V}\). Substituting these values into the transformer equation, we get: \(\frac{16}{V_s} = \frac{250}{1000}\)

Solve for \(V_s\).

To solve for \(V_s\), we can cross-multiply and simplify: \(16 \times 1000 = V_s \times 250\) \(16000 = 250V_s\) Now, divide both sides by 250: \(V_s = \frac{16000}{250}\)

Calculate the emf amplitude in the secondary coil.

After the division, we get the emf amplitude in the secondary coil: \(V_s = 64 \mathrm{V}\) Therefore, the emf amplitude in the secondary coil is \(64 \mathrm{V}\).