Question

an engineer in india (standard household voltage = 220 volts) is designing a transformer for use on her upcoming trip to canada (standard household voltage = 120 volts). if her input coil has 240 turns, how many turns should her output coil have?

Explanation:

Step1: Use transformer voltage - turn ratio formula

The formula for a transformer is \(\frac{V_{in}}{V_{out}}=\frac{N_{in}}{N_{out}}\), where \(V_{in}\) is the input voltage, \(V_{out}\) is the output voltage, \(N_{in}\) is the number of turns in the input coil, and \(N_{out}\) is the number of turns in the output coil.
We are given \(V_{in} = 220\) volts, \(V_{out}=120\) volts, and \(N_{in} = 240\) turns. We need to find \(N_{out}\).

Step2: Rearrange the formula to solve for \(N_{out}\)

From \(\frac{V_{in}}{V_{out}}=\frac{N_{in}}{N_{out}}\), we can cross - multiply to get \(N_{out}=\frac{V_{out}\times N_{in}}{V_{in}}\)
Substitute the given values: \(N_{out}=\frac{120\times240}{220}\)
First, calculate \(120\times240 = 28800\)
Then, \(N_{out}=\frac{28800}{220}=\frac{1440}{11}\approx130.91\)

Answer:

The number of turns in the output coil should be approximately \(131\) turns.