- #1

Gear300

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Circuit is shown in attachement. At t = 0s, switch S is closed. Find a function for the current through the inductor starting from t = 0s.

Using Kirchoff's method, I find that the maximum current through the inductor is .500 A as t approaches infinite and that the total current is 1.50 A. I took in the assumption that from t = 0s and onward, the current through the path with the inductor is proportionally 1/3 of the total current. Then I set up an equation:

E - 3IR1 - IR2 - L*dI/dt = 0, in which E is the emf of the battery, I is the current through the inductor, R1 is the resistor on the top left (4.00 Ohm), R2 is the resistor on the top right (8.00 Ohm), L is the inductance, and dI/dt is a derivative of the current. R1 carries the total current, so its current would be 3 times the current in R2. Using this equation, I set up a differential equation, receiving:

I = .500*(1 - e^(-20t)), in which the maximum current corresponds to the maximum current I got from Kirchoff's method.

However, the answer I'm supposed to get is I = .500*(1 - e^(-10t))...I didn't see anything wrong in my method. Any help?

Using Kirchoff's method, I find that the maximum current through the inductor is .500 A as t approaches infinite and that the total current is 1.50 A. I took in the assumption that from t = 0s and onward, the current through the path with the inductor is proportionally 1/3 of the total current. Then I set up an equation:

E - 3IR1 - IR2 - L*dI/dt = 0, in which E is the emf of the battery, I is the current through the inductor, R1 is the resistor on the top left (4.00 Ohm), R2 is the resistor on the top right (8.00 Ohm), L is the inductance, and dI/dt is a derivative of the current. R1 carries the total current, so its current would be 3 times the current in R2. Using this equation, I set up a differential equation, receiving:

I = .500*(1 - e^(-20t)), in which the maximum current corresponds to the maximum current I got from Kirchoff's method.

However, the answer I'm supposed to get is I = .500*(1 - e^(-10t))...I didn't see anything wrong in my method. Any help?

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