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Chapter 20: Problem 33

A doorbell uses a transformer to deliver an amplitude of \(8.5 \mathrm{V}\) when it is connected to a \(170-\mathrm{V}\) amplitude line. If there are 50 turns on the secondary, (a) what is the turns ratio? (b) How many turns does the primary have?

Short Answer

Expert verified
Answer: The turns ratio is approximately 20, and the primary coil has approximately 1000 turns.

Step by step solution

01

Identify the given information

We are given: - \(V_p = 170 \mathrm{V}\) (voltage of the primary coil) - \(V_s = 8.5 \mathrm{V}\) (voltage of the secondary coil) - \(N_s = 50\) (number of turns in the secondary coil)
02

Calculate the turns ratio

Using the formula for the turns ratio: $$\frac{N_p}{N_s}=\frac{V_p}{V_s}$$ Plug in the given values: $$\frac{N_p}{50}=\frac{170}{8.5}$$ Now, we can solve for the turns ratio, which is the ratio of \(N_p\) to \(N_s\): $$\frac{N_p}{50}=\frac{170}{8.5} \Rightarrow \frac{N_p}{50} \approx 20$$ So, the turns ratio is approximately 20.
03

Find the number of turns in the primary coil

Now that we have the turns ratio, we can find how many turns are in the primary coil. We know the following: $$\frac{N_p}{50} \approx 20$$ Now, we can solve for \(N_p\): $$N_p \approx 20 \times 50 = 1000$$ Therefore, the primary coil has approximately 1000 turns.

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Most popular questions from this chapter

The magnetic field between the poles of an electromagnet is \(2.6 \mathrm{T} .\) A coil of wire is placed in this region so that the field is parallel to the axis of the coil. The coil has electrical resistance \(25 \Omega,\) radius $1.8 \mathrm{cm},\( and length \)12.0 \mathrm{cm} .$ When the current supply to the electromagnet is shut off, the total charge that flows through the coil is \(9.0 \mathrm{mC} .\) How many turns are there in the coil?
A step-down transformer has 4000 turns on the primary and 200 turns on the secondary. If the primary voltage amplitude is \(2.2 \mathrm{kV},\) what is the secondary voltage amplitude?
The largest constant magnetic field achieved in the laboratory is about $40 \mathrm{T}$. (a) What is the magnetic energy density due to this field? (b) What magnitude electric field would have an equal energy density?
A de motor has coils with a resistance of \(16 \Omega\) and is connected to an emf of \(120.0 \mathrm{V}\). When the motor operates at full speed, the back emf is \(72 \mathrm{V}\). (a) What is the current in the motor when it first starts up? (b) What is the current when the motor is at full speed? (c) If the current is \(4.0 \mathrm{A}\) with the motor operating at less than full speed, what is the back emf at that time?
Two solenoids, of \(N_{1}\) and \(N_{2}\) turns respectively, are wound on the same form. They have the same length \(L\) and radius \(r\) (a) What is the mutual inductance of these two solenoids? (b) If an ac current $$I_{1}(t)=I_{\mathrm{m}} \sin \omega t$$ flows in solenoid $$1\left(N_{1} \text { turns }\right)$$ write an expression for the total flux through solenoid \(2 .\) (c) What is the maximum induced emf in solenoid \(2 ?[\text { Hint: Refer to Eq. }(20-7) .]\)
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