Question

A transformer with a primary coil of 1000 turns is used to step up the standard \(170-\mathrm{V}\) amplitude line voltage to a \(220-\mathrm{V}\) amplitude. How many turns are required in the secondary coil?

Short answer

Answer: 1295 turns.

Step-by-step solution

Recall the transformer turns ratio formula

The transformer turns ratio formula is given by: $$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$ Where \(V_p\) is the primary voltage, \(V_s\) is the secondary voltage, \(N_p\) is the primary coil turns, and \(N_s\) is the secondary coil turns.

Plug in the given values

We are given the primary coil turns \(N_p = 1000\), the primary voltage \(V_p = 170\,\mathrm{V}\), and the secondary voltage \(V_s = 220\,\mathrm{V}\). Our task is to find the secondary coil turns \(N_s\). We can plug the values into the formula: $$\frac{170}{220} = \frac{1000}{N_s}$$

Solve for the secondary coil turns

To find \(N_s\), we can cross-multiply and then solve for \(N_s\): $$170 \times N_s = 1000 \times 220$$ $$N_s = \frac{1000 \times 220}{170}$$ $$N_s = 1294.1176$$ Since the number of turns in a coil must be an integer, we round up to the nearest whole number: $$N_s = 1295$$ So, there are 1295 turns required in the secondary coil to step up the voltage from 170V to 220V.