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Answer:
Step-by-step explanation:
Before we even begin it would be very helpful to draw out a simple layout of the circuit. Then we go ahead and apply kirchoffs second law(sum of voltages around a loop must be zero) on the circuit and we obtain the following differential equation,
where V is the electromotive force applied to the LR series circuit, Ldi/dt is the voltage drop across the inductor and Ri is the voltage drop across the resistor. we can re write the equation as,
Then we first solve for the homogeneous part given by,
we obtain,
This is only the solution to the homogeneous part, The final solution would be given by,
where c is some constant, we added this because the right side of the primary differential equation has a constant term given by V/R. We put this in the main differential equation and obtain the value of c as c=V/R by comparing the constants on both sides.if we put in our initial condition of i(0)=0, we obtain , so the overall equation becomes,
where if we just plug in the values given in the question we obtain the answer given below,