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Chapter 28: Problem 37

You're planning to study in Europe, and you want a transformer designed to step \(230-\mathrm{V}\) European power down to \(120 \mathrm{V}\) needed to operate your stereo. (a) If the transformer's primary has 460 turns, how many should the secondary have? (b) You can save money with a transformer whose maximum primary current is \(1.5 \mathrm{A}\). If your stereo draws a maximum of \(3.3 \mathrm{A},\) will this transformer work?

Short Answer

Expert verified
To find the number of turns for the secondary coil, calculate \(N_s = (460 * 120) / 230\). Then, calculate the primary current \(I_p = (460/N_s) * 3.3\) and check if the calculated \(I_p\) is less than or equal to 1.5 Amps to decide if the transformer is suitable.

Step by step solution

01

Calculate Turns for Secondary Coil

First, let's use the transformation formula for voltage which is \(V_p/V_s = N_p/N_s\). By substituting given values, \(230/120 = 460/N_s\). Solving this for \(N_s\), we will have \(N_s = (460 * 120) / 230\). Calculate this value to find the number of turns for the secondary coil.
02

Check if Transformer is Suitable

Now, let's check how much current will be drawn from the primary coil using the formula for transforming current \(I_p/I_s = N_s/N_p\). We need to find out if the primary coil will be able to provide enough current to match the stereo's requirements given that the stereo draws maximum of 3.3 Amps. So, substituting the given values, we will have \(I_p = (N_p/N_s) * I_s = (460/N_s) * 3.3\). After calculating all these values, check if \(I_p\) is less than or equal to 1.5 Amps. If it is, the transformer is suitable. If not, the transformer won't work for the stereo.

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Most popular questions from this chapter

Much of Europe uses AC power at \(230 \mathrm{V}\) rms and \(50 \mathrm{Hz}\). Express this AC voltage in the form of Equation \(28.3,\) taking \(\phi_{V}=0\)

An RLC circuit includes a 1.5 -H inductor and a \(250-\mu \mathrm{F}\) capacitor rated at 400 V. The circuit is connected across a sine-wave generator with \(V_{\mathrm{p}}=32 \mathrm{V} .\) What minimum resistance will ensure that the capacitor voltage does not exceed its rated value when the circuit is at resonance?

A 2.2 -nF capacitor and one of unknown capacitance are in parallel across a \(10-\mathrm{V}\) rms sine-wave generator. At \(1.0 \mathrm{kHz}\), the generator supplies a total current of \(3.4 \mathrm{mA}\) rms. The generator frequency is then decreased until the rms current drops to 1.2 mA. Find (a) the unknown capacitance and (b) the lower frequency.

A power supply like that of Fig. 28.23 is supposed to deliver 22-V DC at a maximum current of 150 mA. The transformer's peak output voltage can charge the capacitor to a full \(22 \mathrm{V},\) and the primary is supplied with \(60-\mathrm{Hz}\) AC. What capacitance will ensure that the output voltage stays within \(3 \%\) of the rated \(22 \mathrm{V} ?\)

A triangle wave swings linearly between voltages \(-V_{\mathrm{p}}\) and \(+V_{\mathrm{p}}\) Show that the rms voltage of a triangle wave is \(V_{\mathrm{p}} / \sqrt{3}\)
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