The figure shows a driven RLC circuit that contains two identical capacitors and

Question

The figure shows a driven RLC circuit that contains two identical capacitors and two switches. The emf amplitude is set at 11.8 V, and the driving frequency is set at 55.1 Hz. With both switches open, the current leads the emf by 31.3 degree. With switch S_1 closed and switch S_2 still open, the emf leads the current by 15.3 degree. With both switches closed, the current amplitude is 452 mA. What are (a) R, (b) C, and (c) L? (a) Number 95.4281756 Units (b) Number 26.6106 Units (c) Numbe2.0006 Unit

Explanation / Answer

Xc = 1/ (2 pi f C)

= 1 / (2 x pi x 55.1 x C)

= 0.00289 / C

XL = 2 pi f L = 346.3 L

Z = R + j(XL - 2Xc)

  
tan31.3 = (2Xc - XL) / R .....(i)

tan15.3 = (XL - Xc) / R ....... (ii)

(i) / (ii) => tan31.3 / tan15.3 = 2Xc - XL / (XL - Xc)

2 Xc - XL = 2.22 XL - 2.22 Xc

4.222 Xc = 3.22 XL

XL = 1.31 Xc

when both switch are close,

Z = XL - Xc

I = V / XL - XC

XL - Xc = 26.1

1.31Xc - Xc = 26.1

Xc = 84.2 Ohm

0.00289 / C = 84.2

C = 34.3 x 10^-6 F ...........Ans (b)

XL = 1.31 Xc = 110.3 ohm

346.3 L = 110.3

L = 0.32 H ...........Ans(c)

tan31.3 = (2Xc - XL) / R = 168.4 - 110.3 / R

R = 95.5 ohm ........Ans(a)

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