Question:
The normal magnetic flux passing through a coil changes with time according to the equation $\phi = 6t^2 - 5t + 1$. What is the magnitude of the induced current at $t = 0.253\, s$ and resistance $10 \, \Omega $ ?
The normal magnetic flux passing through a coil changes with time according to the equation $\phi = 6t^2 - 5t + 1$. What is the magnitude of the induced current at $t = 0.253\, s$ and resistance $10 \, \Omega $ ?
Updated On: May 12, 2024
- 1.2 A
- 0.8 A
- 0.6 A
- 0.2 A
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The Correct Option is D
Solution and Explanation
Here ,
Magnetic flux, $\phi = 6t^2 - 5t + 1$
Resistance, $R = 10\, \Omega$
The induced emf is
$\varepsilon = - \frac{d\phi}{dt} = - \frac{d}{dt} \left(6t^{2} - 5t+ 1\right)=-\left(12t - 5 \right) $
At $t = 0.253 \,s$
$\varepsilon = -(12 \times 0.253 - 5 ) = 1.964 \, V = 2 V$
$\therefore$ Induced current, $ I = \frac{ \varepsilon}{R} = \frac{2}{10} = 0.2 A$
Magnetic flux, $\phi = 6t^2 - 5t + 1$
Resistance, $R = 10\, \Omega$
The induced emf is
$\varepsilon = - \frac{d\phi}{dt} = - \frac{d}{dt} \left(6t^{2} - 5t+ 1\right)=-\left(12t - 5 \right) $
At $t = 0.253 \,s$
$\varepsilon = -(12 \times 0.253 - 5 ) = 1.964 \, V = 2 V$
$\therefore$ Induced current, $ I = \frac{ \varepsilon}{R} = \frac{2}{10} = 0.2 A$
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Concepts Used:
Faradays Laws of Induction
There are two laws, given by Faraday which explain the phenomena of electromagnetic induction:
Faraday's First Law:
Whenever a conductor is placed in a varying magnetic field, an emf is induced. If the conductor circuit is closed, a current is induced, known as the induced current.
Faraday's Second Law:
The Emf induced inside a coil is equal to the rate of change of associated magnetic flux.
This law can be mathematically written as:
∈\(-N {\triangle \phi \over \triangle t}\)
