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Chapter 23: Q45PE (page 861)

An American traveller in New Zealand carries a transformer to convert New Zealand鈥檚 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

Expert verified
  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

01

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.

02

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,

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

03

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\(2\).

04

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 \(0.5A\).

05

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.

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Most popular questions from this chapter

A short circuit to the grounded metal case of an appliance occurs as shown in Figure \({\rm{23}}{\rm{.60}}\). The person touching the case is wet and only has a \({\rm{3}}{\rm{.00 k\Omega }}\) resistance to earth/ground.

(a) What is the voltage on the case if \({\rm{5}}{\rm{.00 mA}}\) flows through the person?

(b) What is the current in the short circuit if the resistance of the earth/ground wire is \({\rm{0}}{\rm{.200 \Omega }}\)?

(c) Will this trigger the \({\rm{20}}{\rm{.0 A}}\) circuit breaker supplying the appliance?

(a) Calculate the self-inductance of a \({\rm{50}}{\rm{.0}}\)cm long, \({\rm{10}}{\rm{.0}}\)cm diameter solenoid having \({\rm{1000}}\) loops. (b) How much energy is stored in this inductor when \({\rm{20}}{\rm{.0}}\) A of current flows through it? (c) How fast can it be turned off if the induced emf cannot exceed \({\rm{3}}{\rm{.00}}\)V?

(a) The plug-in transformer for a laptop computer puts out \(7.50V\) and can supply a maximum current of \(2.00A\). What is the maximum input current if the input voltage is \(240V\)? Assume \(100\% \) efficiency. (b) If the actual efficiency is less than \(100\% \), would the input current need to be greater or smaller? Explain.

Suppose you have a supply of inductors ranging from \(1.00{\rm{ }}nH\) to\(10.0{\rm{ }}H\), and resistors ranging from \(0.100{\rm{ }}\Omega \) to\(1.00{\rm{ }}M\Omega \). What is the range of characteristic \(RL\) time constants you can produce by connecting a single resistor to a single inductor?

A cassette recorder uses a plug-in transformer to convert\(120{\rm{ }}V\)to\(12.0{\rm{ }}V\), with a maximum current output of\(200mA\).

(a) What is the current input?

(b) What is the power input?

(c) Is this amount of power reasonable for a small appliance?
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