What percentage of the initial energy stored in the capacitor in ( Figure 1 ) is

Question

What percentage of the initial energy stored in the capacitor in (Figure 1) is dissipated by the 40 k? resistor? Suppose that R = 35k? .

In the circuit the switch has been closed for a long time before opening at t=0.

Find the value of L so that vo(t) equals 0.5vo(0+) when t = 3.4ms . Take R = 16? .

Find the percentage of the stored energy that has been dissipated in the resistor R when t = 3.4ms .

What percentage of the initial energy stored in the capacitor in (Figure 1) is dissipated by the 40 k? resistor? Suppose that R = 35k? . In the circuit the switch has been closed for a long time before opening at t=0. Find the value of L so that vo(t) equals 0.5vo(0+) when t = 3.4ms . Take R = 16? . Find the percentage of the stored energy that has been dissipated in the resistor R when t = 3.4ms .

Explanation / Answer

all the enrgy will be dissipated by the resistors.

hence the % of energy is directly proportional to square of the current.

hence if current through R is i1 and current through (40+10)=50 kilo ohms is i2,

then i1/i2=50/R=10/7

so energy ratio=(10/7)^2=100/49

so if energy dissipated by 50 kilo ohms is E1, then E2=100*E1/49

now E1+E2=100%

so E1=32.886%

now same current flows through 40 k and 10k resistors.

so energy is directly proportional to their resistance

so energy dissipation ratio=4/1

hence total % energy dissipated through 40k is (4/5)*32.886= 26.31 %

Q2.

as switch is closed for long time, the inductor has become short circuit,
hence current flowing through it=30 mA*(1/(1+9))=3 mA

after opening of the switch, this current will flow through R.

hence v0(0+)=-R*3 mA=-48 volts

now as the voltage will be decreasing exponetially with a time constant of L/R
we get

0.5*V0(0+)=V0(0+)*exp(-3.4*0.001/T)

where T=time constant in seconds

hence T=4.9052 ms

hence L/R=4.9052*0.001
L=78.483 H

as voltage becomes half, 25% of the energy remains.

hence 75% energy is dissipated.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.