From the equation of the power stored in a conductor, we have the right to solve for the differential, dI(t)/dt as:


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To know the math of current decay in an L-R circuit.

You are watching: What is the differential equation satisfied by the current i(t) after time t=0?

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A DC voltage source is associated to a resistor of resistance R and also an inductor through inductance L, developing the circuit presented in the figure. Because that a long time prior to t = 0, the switch has remained in the place shown, so that a existing I0 has been gathered in the circuit through the voltage source. At t = 0 the switch is thrown to remove the voltage resource from the circuit. This problem pertains to the habits of the current from the circuit. This problem involves the habits of the current I (t) with the inductor and the voltage V (t) across the indicator at time t ~ t = 0.

Part A. What is the differential equation satisfied through the present I (t) ~ time t = 0? refer dI(t)/dt in terms of I (t), R, and also L.

Part B. What is the expression for I(t) derived by fixing the differential equation the I(t) satisfied ~ t = 0? Express her answer in terms f the initial present I0 and also L, R, and also t.


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