The current flowing through an inductance coi | vedclass

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Question

(D) The induced emf in an inductor is given by the formula $|e| = L \left| \frac{dI}{dt} ight|$.Given self-inductance $L = 6 	ext{ mH} = 6 	imes 1

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$30 	imes 10^{-4} 	ext{ V}$

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(D) The induced emf in an inductor is given by the formula $|e| = L \left| \frac{dI}{dt} ight|$.Given self-inductance $L = 6 	ext{ mH} = 6 	imes 10^{-3} 	ext{ H}$.From the graph,at $t_1 = 20 	ext{ s}$,the current $I_1 = 4 	ext{ A}$,and at $t_2 = 40 	ext{ s}$,the current $I_2 = 3 	ext{ A}$.The rate of change of current is $\left| \frac{dI}{dt} ight| = \left| \frac{I_2 - I_1}{t_2 - t_1} ight| = \left| \frac{3 - 4}{40 - 20} ight| = \left| \frac{-1}{20} ight| = 0.05 	ext{ A/s}$.Thus,the induced emf is $|e| = (6 	imes 10^{-3} 	ext{ H}) 	imes (0.05 	ext{ A/s}) = 0.3 	imes 10^{-3} 	ext{ V} = 3 	imes 10^{-4} 	ext{ V}$.However,checking the options provided,$3 	imes 10^{-4} 	ext{ V}$ is equivalent to $30 	imes 10^{-5} 	ext{ V}$. Re-evaluating the calculation: $6 	imes 10^{-3} 	imes (1/20) = 6/20 	imes 10^{-3} = 0.3 	imes 10^{-3} = 3 	imes 10^{-4} 	ext{ V}$.Given the options,$30 	imes 10^{-5} 	ext{ V}$ is not listed,but $30 	imes 10^{-4} 	ext{ V}$ is option $D$. Let's re-examine the graph. If the current at $t=40$ was $0$,the change would be $4/20 = 0.2$. $6 	imes 10^{-3} 	imes 0.2 = 1.2 	imes 10^{-3}$. If the current at $t=20$ was $4$ and $t=40$ was $3$,the slope is $1/20$. The calculation $3 	imes 10^{-4} 	ext{ V}$ is correct. Since $30 	imes 10^{-5} 	ext{ V}$ is not an option,and $3 	imes 10^{-4} 	ext{ V}$ is the result,we select the closest magnitude if applicable,or note the discrepancy. Given the options,$30 	imes 10^{-5} 	ext{ V}$ is $3 	imes 10^{-4} 	ext{ V}$. Option $D$ is $30 	imes 10^{-4} 	ext{ V} = 3 	imes 10^{-3} 	ext{ V}$. There might be a typo in the question's options. Assuming the intended answer is $3 	imes 10^{-4} 	ext{ V}$.

The current flowing through an inductance coil of self-inductance $6 \text{ mH}$ at different time instants is as shown. The emf induced between $t=20 \text{ s}$ and $t=40 \text{ s}$ is nearly

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