6.9 A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?

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Payal Gupta | Contributor-Level 10

4 months ago

6.9 Mutual inductance of a pair of coils, $μ$ = 1.5 H

Initial current, $I_{1}$ = 0 A

Final current, $I_{2}$ = 20 A

Change in current, dI = $I_{2}$ - $I_{1}$ = 20 A

Time taken for change, dt = 0.5 s

From the relation of induced emf e = $\frac{d \emptyset}{d t}$ , where $d \emptyset$ is the change in the flux linkage with the coil ……………(1)

The relation between emf and mutual inductance is e = $μ \frac{d I}{d t}$ …………. (2)

Combining equations (1) and (2), we get

$\frac{d \emptyset}{d t} = μ \frac{d I}{d t}$ or $d \emptyset = μ d I$ = 1.5 $\times 20$ = 30 Wb

Hence, the change in the flux linkage is 30 Wb

6.9 Mutual inductance of a pair of coils, <math><mi>μ</mi></math> = 1.5 HInitial current, <math><msub><mrow><mrow><mi>I</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> = 0 AFinal current, <math><msub><mrow><mrow><mi>I</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math> = 20 AChange in current, dI = <math><msub><mrow><mrow><mi>I</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math> - <math><msub><mrow><mrow><mi>I</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> = 20 ATime taken for change, dt = 0.5 sFrom the relation of induced emf e = <math><mfrac><mrow><mrow><mi>d</mi><mi>∅</mi></mrow></mrow><mrow><mrow><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></math> , where <math><mi>d</mi><mi>∅</mi></math> is the change in the flux linkage with the coil ……………(1)The relation between emf and mutual inductance is e = <math><mi>μ</mi><mfrac><mrow><mrow><mi>d</mi><mi>I</mi></mrow></mrow><mrow><mrow><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></math> …………. (2)Combining equations (1) and (2), we get<math><mfrac><mrow><mrow><mi>d</mi><mi>∅</mi></mrow></mrow><mrow><mrow><mi>d</mi><mi>t</mi></mrow></mrow></mfrac><mo>=</mo><mi></mi><mi>μ</mi><mfrac><mrow><mrow><mi>d</mi><mi>I</mi></mrow></mrow><mrow><mrow><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></math> or <math><mi>d</mi><mi>∅</mi><mo>=</mo><mi></mi><mi>μ</mi><mi>d</mi><mi>I</mi></math> = 1.5 <math><mo>×</mo><mn>20</mn></math> = 30 WbHence, the change in the flux linkage is 30 Wb

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6.9 A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?

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