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A $25-\mathrm{mH}$ inductor, an $8.0-\Omega$ resistor, and a $6.0-\mathrm{V}$ battery are connected in series as in Figure $\mathrm{P} 20.43 .$ The switch is closed at $t=0 .$ Find the voltage drop across the resistor (a) at $t=0$ and (b) after one time constant has passed. Also, find the voltage drop across the inductor $(\mathrm{c})$ at $l=0$ and $(\mathrm{d})$ after one time constant has elapsed.

a. 0.0 V

b. 3.8 \mathrm{V}

c. 6.0 \mathrm{V}

d. 2.2 \mathrm{V}

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for part A were asked to find the voltage drop across the resistor. At T equals zero seconds. And after one time, constant has passed. Okay, well, the voltage across the resistor, we'll call it Visa Bar is equal to the potential supplied by the battery up salud times one minus E to the minus t, which is the amount of time divided by the time constant towel. So when t is equal to zero, this is equal to the battery times one minus e to the zero E to the zero is equal the ones This is at the battery times one minus one, which is equal to zero weaken box I dent is their solution for a for part B were asked to find the potential across the resistor when the time that has passed is equal to one time constant. So this is gonna be absolute times would might this e to the minus towel over Tao, which is e to the minus one. So carrying out this expression, we find that B is equal to 3.8 volts. Weekend box. It is the solution for question. Be question C asked us to find the potential across the induct er will call that Visa Bell. This is equal to absolute minus I r. So using Kirchoff ce rule, this is equal to the battery minus potential across the resistor which is equal to playing in the value for the potential across three sister of the battery minus herbal supplied by one minus E to the minus t over towel. This comes out to equal absolutely tyrants e to the minus t over towel. Well, for part C were asked to consider when t is equal to zero. So this is equal to Absalon, which is equal to the six Volt. So it's just the potential the battery become box. It is their solution for seat and finally party. We're gonna use the same equation we just found for the potential across the induct er times e to the minus. Well, this is t over towel, but this is when tea is equal. That house, this is minus Would this comes out to equal 2.2 bolts weaken box and it is your solution