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?
Solution and Explanation
Mutual inductance of a pair of coils, \(\mu\) = 1.5 H
Initial current, \(I_1\) = 0 A
Final current \(I_2\)= 20 A
Change in current, \(dI\)= \(I_1-I_2\) = 20-0 = 20A
Time taken for the change, t = 0.5 s
Induced emf, e=\(\frac{d\phi}{dt}\) ...(1)
Where \(d\phi\) is the change in the flux linkage with the coil.
Emf is related with mutual inductance as:
e= \(\mu\frac{d\phi}{dt}\) ...(2)
Equating equations (1) and (2), we get
\(\frac{d\phi}{dt}\) =\(\mu\frac{d\phi}{dt}\)
\(d\phi\) = 1.5 x (20)
=30Wb
Hence, the change in the flux linkage is 30 Wb
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Concepts Used:
Inductance
Inductance is a key parameter in electrical and electronic circuit designs. Like resistance and capacitance, it is a basic electrical measurement that affects all circuits to some degree.
Inductance is used in many areas of electrical and electronic systems and circuits. The electronic components can be in a variety of forms and may be called by a variety of names: coils, inductors, chokes, transformers, . . . Each of these may also have a variety of different variants: with and without cores and the core materials may be of different types.
There are two ways in which inductance is used:
- Self-inductance: Self-inductance is the property of a circuit, often a coil, whereby a change in current causes a change in voltage in that circuit due to the magnetic effect of caused by the current flow. It can be seen that self-inductance applies to a single circuit - in other words it is an inductance, typically within a single coil. This effect is used in single coils or chokes.
- Mutual-inductance: Mutual inductance is an inductive effect where a change in current in one circuit causes a change in voltage across a second circuit as a result of a magnetic field that links both circuits. This effect is used in transformers.