Flux ϕ(in weber) in a closed circuit of resistance 10 Ωvaries with time t (in seconds) according

step 1 Hello students in this question we have given the flux in the closed loop 5 equals to 6 t square

Flux ϕ(in weber) in a closed circuit of resistance 10...

Flux $\phi$ (in weber) in a closed circuit of resistance $10 \Omega$ varies with time $t$ (in seconds) according to the equation $\phi=6 t^{2}-5 t+1$. The magnitude of the induced current in the circuit at $t=0.25 \mathrm{~s}$ is (A) $0.2 \mathrm{~A}$ (B) $0.6 \mathrm{~A}$ (C) $0.8 \mathrm{~A}$ (D) $1.2 \mathrm{~A}$

Flux $\phi$ (in weber) in a closed circuit of resistance $10 \Omega$ varies with time $t$ (in seconds) according to the equation $\phi=6 t^{2}-5 t+1$. The magnitude of the induced current in the circuit at $t=0.25 \mathrm{~s}$ is
(A) $0.2 \mathrm{~A}$
(B) $0.6 \mathrm{~A}$
(C) $0.8 \mathrm{~A}$
(D) $1.2 \mathrm{~A}$

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Key Concepts

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a change in magnetic flux through a circuit induces an electromotive force (EMF) in the circuit. The induced EMF is proportional to the negative rate of change of the magnetic flux, which is fundamental to understanding how varying magnetic fields generate currents in closed circuits.

Time Derivative of Magnetic Flux

The rate of change of magnetic flux with respect to time is computed using differentiation. This derivative is essential because it quantifies how quickly the flux changes, and according to Faraday's Law, it directly determines the magnitude of the induced EMF.

Ohm's Law

Ohm's Law relates the voltage (or EMF) across a circuit to the current flowing through it and the resistance of the circuit. When an induced EMF is present due to a changing magnetic flux, Ohm's Law (I = EMF/R) is used to calculate the resulting induced current, connecting the concepts of electromagnetic induction and electrical circuit behavior.

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