7.23 A power transmission line feeds input power at 2300 V to a step-down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V?
From the relation of voltage and number of turns, we get
= or = = 400
Hence, there are 400 turns in the second winding.
<p><strong>7.23 </strong>Input voltage, <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>V</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math></span> = 2300 V</p><p>Number of turns in primary coil, <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>n</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math></span> = 4000</p><p>Output voltage, <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>V</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></span> = 230 V</p><p>Number of turns in secondary coil = <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>n</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></span></p><p>From the relation of voltage and number of turns, we get</p><p><span title="Click to copy mathml"><math><mfrac><mrow><mrow><msub><mrow><mrow><mi>V</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>V</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><msub><mrow><mrow><mi>n</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>n</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span> or <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>n</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>=</mo><mi></mi><mfrac><mrow><mrow><msub><mrow><mrow><mi>n</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub><msub><mrow><mrow><mi>V</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>V</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>4000</mn><mo>×</mo><mn>230</mn></mrow></mrow><mrow><mrow><mn>2300</mn></mrow></mrow></mfrac></math></span> = 400</p><p>Hence, there are 400 turns in the second winding.</p>
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