Transformers: Practice Problem & Solution
The primary winding of a transformer has 500 turns whereas its secondary has 5000 turns. The primary is connected to an A.C. supply 20 V, 50 Hz. The secondary will have an output of (1997)
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Transformers. Understanding the underlying formula is key to arriving at the correct answer below:
Output voltage $V_s = V_p \left(\frac{N_s}{N_p}\right) = 20 \times \left(\frac{5000}{500}\right) = 200 V$.
The frequency of an alternating current does not change when passing through a transformer.
Therefore, the output will be $200 V, 50 Hz$.
Detailed Solution (Best of Understanding Complex Concepts)
Key Concepts
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Transformer Voltage Ratio: In an ideal transformer, the ratio of the secondary voltage ($V_s$) to the primary voltage ($V_p$) is directly proportional to the ratio of the number of turns in the secondary winding ($N_s$) to the number of turns in the primary winding ($N_p$).$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$
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Frequency in a Transformer: A transformer operates on the principle of mutual induction. While it steps up or steps down the voltage and current, it does not change the frequency of the alternating current. The frequency of the output (secondary) is exactly the same as the frequency of the input (primary).
Step-by-Step Solution
1. Identify the given parameters:
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Number of turns in the primary winding ($N_p$) = 500
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Number of turns in the secondary winding ($N_s$) = 5000
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Primary voltage ($V_p$) = 20 V
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Primary frequency ($f_p$) = 50 Hz
2. Calculate the secondary voltage ($V_s$):
Rearrange the transformer equation to solve for $V_s$:
$$V_s = V_p \times \left(\frac{N_s}{N_p}\right)$$
Substitute the given values into the equation:
$$V_s = 20 \times \left(\frac{5000}{500}\right)$$
$$V_s = 20 \times 10$$
$$V_s = 200 \text{ V}$$
3. Determine the secondary frequency ($f_s$):
Since the transformer does not change the frequency of the AC supply, the secondary frequency remains the same as the primary frequency:
$$f_s = 50 \text{ Hz}$$
The secondary will have an output of 200 V, 50 Hz.
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