Question

An American traveller in New Zealand carries a transformer to convert New Zealand’s standard\(240{\rm{ }}V\)to\(120{\rm{ }}V\)so that she can use some small appliances on her trip. (a) What is the ratio of turns in the primary and secondary coils of her transformer?

(b) What is the ratio of input to output current?

(c) How could a New Zealander traveling in the United States use this same transformer to power her\(240{\rm{ }}V\)appliances from\(120{\rm{ }}V\)?

Short answer

1. Ratio of turns in the primary and secondary coils is\(2\).
2. Ratio of input to output current value is\(0.5A\).
3. Same transformer can be used with reversing primary and secondary.

Step-by-step solution

Definition of current and resistance 

Current is the term used to describe the speed at which charge moves. Resistance is the propensity of a substance to oppose the flow of charge.

Given information and Formula to be used 

a)

\(\begin{array}{l}{V_p} = 240\;V\\{V_s} = 120\;V\end{array}\)

Transformer equation,

\(\frac{{{V_s}}}{{{V_p}}} = \frac{{{N_s}}}{{{N_p}}}\)

b)

\(\begin{array}{l}{V_p} = 240\;V\\{V_s} = 120\;V\end{array}\)

Transformer equation,

\(\frac{{{V_s}}}{{{V_p}}} = \frac{{{I_p}}}{{{I_s}}}\)

c)

\(\begin{array}{l}{V_p} = 240\;V\\{V_s} = 120\;V\end{array}\)

Transformer equation,

\(\frac{{{V_s}}}{{{V_p}}} = \frac{{{N_s}}}{{{N_p}}}\)

Ratio of Turns 

a)

Consider the transformer equation,

\(\begin{array}{c}\frac{{{V_s}}}{{{V_p}}} = \frac{{{N_s}}}{{{N_p}}}\\\frac{{120}}{{240}} = \frac{{{N_s}}}{{{N_p}}}\\\frac{{{N_p}}}{{{N_s}}} = 2\end{array}\)

Therefore, Ratio of turns in the primary and secondary coils is\(2\).

Ratio of Current

b)

Consider the transformer equation

\(\begin{array}{c}\frac{{{V_s}}}{{{V_p}}} = \frac{{{I_p}}}{{{I_s}}}\\\frac{{120}}{{240}} = \frac{{{I_p}}}{{{I_s}}}\\\frac{{{I_p}}}{{{I_s}}} = 0.5\end{array}\)

Therefore, Ratio of input to output current value is \(0.5A\).

Use of the transformer

c)

Consider the transformer equation,

\(\begin{array}{c}\frac{{{V_s}}}{{{V_p}}} = \frac{{{N_s}}}{{{N_p}}}\\\frac{{240}}{{120}} = \frac{{{N_s}}}{{{N_p}}}\\\frac{{{N_p}}}{{{N_s}}} = 0.5\end{array}\)

Therefore, same transformer can be used with reversing primary and secondary.