1. Three resistors with resistances R1 = 8.0 ?, R2 = 83.0 ? and R3 = 16.0 ? are

Question

1. Three resistors with resistances R1 = 8.0 ?, R2 = 83.0 ? and R3 = 16.0 ? are placed along the sides of a triangle as shown in circuit 1. What are the values of the resistances Ra, Rb and Rc that would provide an equivalent circuit as arranged in circuit 2?

2. You charge an initially uncharged 78.1-mF capacitor through a 20.5-? resistor by means of a 9.00-V battery having negligible internal resistance. Find the time constant of the circuit. What is the charge of the capacitor 1.53 time constants after the circuit is closed? What is the charge after a long time?

Explanation / Answer

1.

In figure which one is Ra & Rb and Rc are not visible ,so i am guessing

In Delta to Star conversion

Ra=R1R2/(R1+R2+R3)=8+83/(8+83+16) =0.85 ohms

Rb=R1R3/(R1+R2+R3)=16+83/(8+83+16)=0.9252 ohms

RC=R2R3/(R1+R2+R3)=16+8/(8+83+16)=0.2243 ohms

2.

a)

TIme Constant

T=RC =20.5*78.1*10-3=1.6 seconds

b)

Maximum Charge

Qmax=CV =78.1*10-3*9=0.7029 C=0.703 C (approx)

Charge at t=1.53T

Q=Qmax[1-e-t/T]=0.703[1-e-1.53]

Q=0.551 C

c)

Qmax=0.703 C

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