## Circuit Lab B/C

Cathy-TJ
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### Re: Circuit Lab B/C

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mjcox2000
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### Re: Circuit Lab B/C

Note: this problem requires calculus. (It's possible there's a particularly clever solution that bypasses the calculus, but I can't think of one.)

You are an electrical engineer tasked with charging a capacitor $C$ , which is connected in series with resistor $R_s$ and in parallel with resistor $R_p$ . You want to charge the capacitor to a final voltage $V_f$ , and you have at your disposal a current source $I$ . (See the diagram for the circuit configuration, and note that at time $t=0$ , the capacitor is fully discharged. Also note that $I$ is constant; i.e. the current cannot vary with time.)

In the aim of efficiency, you want to dissipate as little power as possible in the resistors as you charge the capacitor to voltage $V_f$ . However, your colleague, who designed the circuit with $R_s$ , $R_p$ , and $C$ and chose the value of $V_f$ , won't let you change any of those values. The only value you can play around with is the charging current $I$ .

a) Find an equation, in terms of $C$ , $R_s$ , $R_p$ , and $V_f$ , and $I$ , for the time $t_f$ at which the capacitor is fully charged to voltage $V_f$ .

b) Find an equation, in terms of $C$ , $R_s$ , $R_p$ , and $V_f$ , and $I$ , for the amount of power dissipated in the resistors in the course of charging the capacitor to voltage $V_f$ .

c) Find an equation, in terms of $C$ , $R_s$ , $R_p$ , and $V_f$ , for the value of $I$ that offers minimum power dissipation. (I'm not convinced this part has a closed-form solution -- if not, do what you can.)
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### Re: Circuit Lab B/C

Note: this problem requires calculus. (It's possible there's a particularly clever solution that bypasses the calculus, but I can't think of one.)

You are an electrical engineer tasked with charging a capacitor $C$ , which is connected in series with resistor $R_s$ and in parallel with resistor $R_p$ . You want to charge the capacitor to a final voltage $V_f$ , and you have at your disposal a current source $I$ . (See the diagram for the circuit configuration, and note that at time $t=0$ , the capacitor is fully discharged. Also note that $I$ is constant; i.e. the current cannot vary with time.)

In the aim of efficiency, you want to dissipate as little power as possible in the resistors as you charge the capacitor to voltage $V_f$ . However, your colleague, who designed the circuit with $R_s$ , $R_p$ , and $C$ and chose the value of $V_f$ , won't let you change any of those values. The only value you can play around with is the charging current $I$ .

a) Find an equation, in terms of $C$ , $R_s$ , $R_p$ , and $V_f$ , and $I$ , for the time $t_f$ at which the capacitor is fully charged to voltage $V_f$ .

b) Find an equation, in terms of $C$ , $R_s$ , $R_p$ , and $V_f$ , and $I$ , for the amount of power dissipated in the resistors in the course of charging the capacitor to voltage $V_f$ .

c) Find an equation, in terms of $C$ , $R_s$ , $R_p$ , and $V_f$ , for the value of $I$ that offers minimum power dissipation. (I'm not convinced this part has a closed-form solution -- if not, do what you can.)

Not really sure if I'm on the right track but

mjcox2000
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### Re: Circuit Lab B/C

UTF-8 U+6211 U+662F wrote:
Note: this problem requires calculus. (It's possible there's a particularly clever solution that bypasses the calculus, but I can't think of one.)

You are an electrical engineer tasked with charging a capacitor $C$ , which is connected in series with resistor $R_s$ and in parallel with resistor $R_p$ . You want to charge the capacitor to a final voltage $V_f$ , and you have at your disposal a current source $I$ . (See the diagram for the circuit configuration, and note that at time $t=0$ , the capacitor is fully discharged. Also note that $I$ is constant; i.e. the current cannot vary with time.)

In the aim of efficiency, you want to dissipate as little power as possible in the resistors as you charge the capacitor to voltage $V_f$ . However, your colleague, who designed the circuit with $R_s$ , $R_p$ , and $C$ and chose the value of $V_f$ , won't let you change any of those values. The only value you can play around with is the charging current $I$ .

a) Find an equation, in terms of $C$ , $R_s$ , $R_p$ , and $V_f$ , and $I$ , for the time $t_f$ at which the capacitor is fully charged to voltage $V_f$ .

b) Find an equation, in terms of $C$ , $R_s$ , $R_p$ , and $V_f$ , and $I$ , for the amount of power dissipated in the resistors in the course of charging the capacitor to voltage $V_f$ .

c) Find an equation, in terms of $C$ , $R_s$ , $R_p$ , and $V_f$ , for the value of $I$ that offers minimum power dissipation. (I'm not convinced this part has a closed-form solution -- if not, do what you can.)

Not really sure if I'm on the right track but

You're on the right track, but
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### Re: Circuit Lab B/C

mjcox2000 wrote:
You're on the right track, but

Agh! Well that sucks.
Take Two

mjcox2000
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### Re: Circuit Lab B/C

UTF-8 U+6211 U+662F wrote:
mjcox2000 wrote:
You're on the right track, but

Agh! Well that sucks.
Take Two

That's right!
A few notes

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### Re: Circuit Lab B/C

Explain how you could solve for the resistance between two ends of a bridge circuit using Kirchoff's rules.

wec01
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### Re: Circuit Lab B/C

UTF-8 U+6211 U+662F wrote:Explain how you could solve for the resistance between two ends of a bridge circuit using Kirchoff's rules.

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UTF-8 U+6211 U+662F
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### Re: Circuit Lab B/C

wec01 wrote:
UTF-8 U+6211 U+662F wrote:Explain how you could solve for the resistance between two ends of a bridge circuit using Kirchoff's rules.

Yep, your turn. Also mention source injection , as applying Kirchoff's laws is rather difficult without it.

wec01
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### Re: Circuit Lab B/C

Calculate the values of I1, I2, and I3 given:

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Cathy-TJ
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### Re: Circuit Lab B/C

wec01 wrote:

Calculate the values of I1, I2, and I3 given:

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mjcox2000
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### Re: Circuit Lab B/C

Edit: Cathy-TJ beat me to an answer.
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wec01
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### Re: Circuit Lab B/C

Cathy-TJ wrote:
wec01 wrote:

Calculate the values of I1, I2, and I3 given:

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Cathy-TJ
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### Re: Circuit Lab B/C

Calculate the resistance between terminals A and B in the infinite chain of resistors where all resistors are 1 ohm.
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mjcox2000
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### Re: Circuit Lab B/C

Cathy-TJ wrote:Calculate the resistance between terminals A and B in the infinite chain of resistors where all resistors are 1 ohm.