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Chapter 14: Problem 2056

A primary winding of transformer has 500 turns whereas its secondary has 5000 turns. Primary is connected to ac supply of \(20 \mathrm{~V}, 50 \mathrm{~Hz}\) The secondary output of (a) \(200 \mathrm{~V}, 25 \mathrm{~Hz}\) (b) \(200 \mathrm{~V}, 50 \mathrm{~Hz}\) (c) \(2 \mathrm{~V}, 100 \mathrm{~Hz}\) (d) \(2 \mathrm{~V}, 50 \mathrm{~Hz}\)

Short Answer

Expert verified
The correct output on the secondary winding of the transformer is \(200 V, 50 Hz\).

Step by step solution

01

Understanding the transformer formula

The transformer formula relates the primary and secondary voltage, their frequency, and the ratio of the number of turns in the primary and secondary windings, as follows: \(V_p / V_s = N_p / N_s\) Where: - \(V_p\) is primary voltage - \(V_s\) is secondary voltage - \(N_p\) is the number of primary turns - \(N_s\) is the number of secondary turns Now let's determine what options are correct.
02

Option (a)

In this option, the secondary voltage is given as \(200 V\) and frequency as \(25 Hz\). Given: \(V_p = 20 V\), \(N_p = 500 \), \(N_s = 5000\) Using the transformer formula: \(20 / 200 = 500 / 5000\) \(1 / 10 = 1 / 10\) This equation is true, so let's check the frequency. Since the transformer is ideal the frequency remains the same in both primary and secondary windings, but in this option \(25 Hz\) is different from the given primary frequency (\(50 Hz\)), so option (a) is not correct.
03

Option (b)

In this option, the secondary voltage is given as \(200 V\) and frequency as \(50 Hz\). Using the transformer formula: \(20 / 200 = 500 / 5000\) \(1 / 10 = 1 / 10\) This equation is true, and the frequency remains the same (\(50 Hz\)) as the primary frequency. Therefore, option (b) is correct.
04

Option (c)

In this option, the secondary voltage is given as \(2 V\) and frequency as \(100 Hz\). Using the transformer formula: \(20 / 2 = 500 / 5000\) \(10 / 1 \neq 1 / 10\) This equation is not true, and the frequency is also different from the primary frequency (\(50 Hz\)), so option (c) is not correct.
05

Option (d)

In this option, the secondary voltage is given as \(2 V\) and frequency as \(50 Hz\). Using the transformer formula: \(20 / 2 = 500 / 5000\) \(10 / 1 \neq 1 / 10\) This equation is not true, but the frequency remains the same (\(50 Hz\)). However, since the voltage ratio is not correct, option (d) is not correct. #Conclusion# The correct output on the secondary winding of the transformer is given by option (b): \(200 V, 50 Hz\).

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