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6.3E: The RLC Circuit (Exercises)

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Q6.3.1

In Exercises 6.3.1-6.3.5 find the current in the RLC circuit, assuming that E(t)=0 for t>0.

1. R=3 ohms;   L=.1 henrys;   C=.01 farads; Q0=0 coulombs;  I0=2 amperes.

2. R=2 ohms;   L=.05 henrys;   C=.01 farads’; Q0=2 coulombs;  I0=2 amperes.

3. R=2 ohms;   L=.1 henrys;   C=.01 farads; Q0=2 coulombs;  I0=0 amperes.

4. R=6 ohms;   L=.1 henrys;   C=.004 farads’; Q0=3 coulombs;  I0=10 amperes.

5. R=4 ohms;   L=.05 henrys;   C=.008 farads; Q0=1 coulombs;  I0=2 amperes.

Q6.3.2

In Exercises 6.3.6-6.3.10 find the steady state current in the circuit described by the equation.

6. 110Q+3Q+100Q=5cos10t5sin10t

7. 120Q+2Q+100Q=10cos25t5sin25t

8. 110Q+2Q+100Q=3cos50t6sin50t

9. 110Q+6Q+250Q=10cos100t+30sin100t

10. 120Q+4Q+125Q=15cos30t30sin30t

Q6.3.3

11. Show that if E(t)=Ucosωt+Vsinωt where U and V are constants then the steady state current in the RLC circuit shown in Figure 6.3.1 is Ip=ω2RE(t)+(1/CLω2)E(t)Δ, where Δ=(1/CLω2)2+R2ω2.

12. Find the amplitude of the steady state current Ip in the RLC circuit shown in Figure 6.3.1 if E(t)=Ucosωt+Vsinωt, where U and V are constants. Then find the value ω0 of ω maximizes the amplitude, and find the maximum amplitude.

Q6.3.4

In Exercises 6.3.13-6.3.17 plot the amplitude of the steady state current against ω. Estimate the value of ω that maximizes the amplitude of the steady state current, and estimate this maximum amplitude. HINT: You can confirm your results by doing Exercise 6.3.12.

13. 110Q+3Q+100Q=Ucosωt+Vsinωt

14. 120Q+2Q+100Q=Ucosωt+Vsinωt

15. 110Q+2Q+100Q=Ucosωt+Vsinωt

16. 110Q+6Q+250Q=Ucosωt+Vsinωt

17. 120Q+4Q+125Q=Ucosωt+Vsinωt


This page titled 6.3E: The RLC Circuit (Exercises) is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench via source content that was edited to the style and standards of the LibreTexts platform.

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