Question:
Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation $I = I_0 sin \omega t, \, $ where $I_0= 10 A $ and $ \omega= 100 \pi$ rad/sec. The maximum value ofe.m.f. in the second coil is
Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation $I = I_0 sin \omega t, \, $ where $I_0= 10 A $ and $ \omega= 100 \pi$ rad/sec. The maximum value ofe.m.f. in the second coil is
Updated On: Aug 1, 2022
- $\pi$
- $5\pi$
- $2\pi$
- $4\pi$
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The Correct Option is B
Solution and Explanation
As $|\in|=M\frac{dI}{dt}=M\frac{d}{dt}(I_0sin \, \omega t)=MI_0\omega cos \omega t$
$\therefore \, \in_{max}=0.005\times10\times100 \pi\times1=5\pi.$
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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.