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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

In this problem, you derive the expression for the self inductance of a long solenoid [Eq. \((20-15 a)] .\) The solenoid has \(n\) turns per unit length, length \(\ell,\) and radius \(r\) Assume that the current flowing in the solenoid is \(I\) (a) Write an expression for the magnetic field inside the solenoid in terms of \(n, \ell, r, I,\) and universal constants. (b) Assume that all of the field lines cut through each turn of the solenoid. In other words, assume the field is uniform right out to the ends of the solenoid-a good approximation if the solenoid is tightly wound and sufficiently long. Write an expression for the magnetic flux through one turn. (c) What is the total flux linkage through all turns of the solenoid? (d) Use the definition of self-inductance [Eq. \((20-14)]\) to find the self inductance of the solenoid.
A coil has an inductance of \(0.15 \mathrm{H}\) and a resistance of 33 \(\Omega\). The coil is connected to a 6.0 - \(V\) battery. After a long time elapses, the current in the coil is no longer changing. (a) What is the current in the coil? (b) What is the energy stored in the coil? (c) What is the rate of energy dissipation in the coil? (d) What is the induced emf in the coil?
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 horizontal desk surface measures \(1.3 \mathrm{m} \times 1.0 \mathrm{m} .\) If Earth's magnetic field has magnitude \(0.44 \mathrm{mT}\) and is directed \(65^{\circ}\) below the horizontal, what is the magnetic flux through the desk surface?
A solenoid is \(8.5 \mathrm{cm}\) long, \(1.6 \mathrm{cm}\) in diameter, and has 350 turns. When the current through the solenoid is \(65 \mathrm{mA},\) what is the magnetic flux through one turn of the solenoid?
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