Question:
A solenoid has $2000$ turns wound over a length of $0.30\, m$ . The area of its cross-section is $1.2 ? 10^{-3}\, m^2$. Around its central section, a coil of $300$ turn is wound. If an initial current of $2A$ in the solenoid is reversed in $0.25\, s$, then the emf induced in the coil is
A solenoid has $2000$ turns wound over a length of $0.30\, m$ . The area of its cross-section is $1.2 ? 10^{-3}\, m^2$. Around its central section, a coil of $300$ turn is wound. If an initial current of $2A$ in the solenoid is reversed in $0.25\, s$, then the emf induced in the coil is
Updated On: Apr 15, 2024
- $6 ? 10^{-4}\, V$
- $4.8 ? 10^{-3}\, V$
- $6 ? 10^{-2}\, V$
- $48\,mV$
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The Correct Option is D
Solution and Explanation
Induced emf $e=M \frac{di}{dt}$
$=\frac{\mu_{0}\,N_{1}\,N_{2}\,A}{l}. \frac{di}{dt}$
$=\frac{4\pi\times10^{-7}\times2000\times300\times1.2\times10^{-3}}{0.30}$
$\times\frac{\left|2-\left(-2\right)\right|}{0.25}$
$=48.2\times10^{-3}\,V=48\,mV$
$=\frac{\mu_{0}\,N_{1}\,N_{2}\,A}{l}. \frac{di}{dt}$
$=\frac{4\pi\times10^{-7}\times2000\times300\times1.2\times10^{-3}}{0.30}$
$\times\frac{\left|2-\left(-2\right)\right|}{0.25}$
$=48.2\times10^{-3}\,V=48\,mV$
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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.