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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 component of the external magnetic field along the central axis of a 50 -turn coil of radius \(5.0 \mathrm{cm}\) increases from 0 to 1.8 T in 3.6 s. (a) If the resistance of the coil is \(2.8 \Omega,\) what is the magnitude of the induced current in the coil? (b) What is the direction of the current if the axial component of the field points away from the viewer?
A \(0.67 \mathrm{mH}\) inductor and a \(130 \Omega\) resistor are placed in series with a \(24 \mathrm{V}\) battery. (a) How long will it take for the current to reach \(67 \%\) of its maximum value? (b) What is the maximum energy stored in the inductor? (c) How long will it take for the energy stored in the inductor to reach \(67 \%\) of its maximum value? Comment on how this compares with the answer in part (a).
The primary coil of a transformer has 250 turns; the secondary coil has 1000 turns. An alternating current is sent through the primary coil. The emf in the primary is of amplitude \(16 \mathrm{V}\). What is the emf amplitude in the secondary? (tutorial: transformer)
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?
Calculate the equivalent inductance \(L_{\mathrm{eq}}\) of two ideal inductors, \(L_{1}\) and \(L_{2},\) connected in parallel in a circuit. Assume that their mutual inductance is negligible. [Hint: Imagine replacing the two inductors with a single equivalent inductor \(L_{\mathrm{eq}} .\) How is the emf in the parallel equivalent related to the emfs in the two inductors? What about the currents? \(]\)
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