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Chapter 20: Problem 36

A transformer with a primary coil of 1000 turns is used to step up the standard \(170-\mathrm{V}\) amplitude line voltage to a \(220-\mathrm{V}\) amplitude. How many turns are required in the secondary coil?

Short Answer

Expert verified
Answer: 1295 turns.

Step by step solution

01

Recall the transformer turns ratio formula

The transformer turns ratio formula is given by: $$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$ Where \(V_p\) is the primary voltage, \(V_s\) is the secondary voltage, \(N_p\) is the primary coil turns, and \(N_s\) is the secondary coil turns.
02

Plug in the given values

We are given the primary coil turns \(N_p = 1000\), the primary voltage \(V_p = 170\,\mathrm{V}\), and the secondary voltage \(V_s = 220\,\mathrm{V}\). Our task is to find the secondary coil turns \(N_s\). We can plug the values into the formula: $$\frac{170}{220} = \frac{1000}{N_s}$$
03

Solve for the secondary coil turns

To find \(N_s\), we can cross-multiply and then solve for \(N_s\): $$170 \times N_s = 1000 \times 220$$ $$N_s = \frac{1000 \times 220}{170}$$ $$N_s = 1294.1176$$ Since the number of turns in a coil must be an integer, we round up to the nearest whole number: $$N_s = 1295$$ So, there are 1295 turns required in the secondary coil to step up the voltage from 170V to 220V.

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Most popular questions from this chapter

The current in a \(0.080-\mathrm{H}\) solenoid increases from \(20.0 \mathrm{mA}\) to \(160.0 \mathrm{mA}\) in \(7.0 \mathrm{s} .\) Find the average emf in the solenoid during that time interval.
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?
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?
A 2 -m-long copper pipe is held vertically. When a marble is dropped down the pipe, it falls through in about 0.7 s. A magnet of similar size and shape takes much longer to fall through the pipe. (a) As the magnet is falling through the pipe with its north pole below its south pole, what direction do currents flow around the pipe above the magnet? Below the magnet (CW or CCW as viewed from the top)? (b) Sketch a graph of the speed of the magnet as a function of time. [Hint: What would the graph look like for a marble falling through honey?]
A \(0.30-\mathrm{H}\) inductor and a \(200.0-\Omega\) resistor are connected in series to a \(9.0-\mathrm{V}\) battery. (a) What is the maximum current that flows in the circuit? (b) How long after connecting the battery does the current reach half its maximum value? (c) When the current is half its maximum value, find the energy stored in the inductor, the rate at which energy is being stored in the inductor, and the rate at which energy is dissipated in the resistor. (d) Redo parts (a) and (b) if, instead of being negligibly small, the internal resistances of the inductor and battery are \(75 \Omega\) and \(20.0 \Omega\) respectively.
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