resistor & capacitor

logistic_guy

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A 1.20\displaystyle 1.20-kΩ\displaystyle \text{k}\Omega resistor and a 6.8\displaystyle 6.8-μF\displaystyle \mu\text{F} capacitor are connected in series to an ac source. Calculate the impedance of the circuit if the source frequency is (a) 60 Hz;\displaystyle \bold{(a)} \ 60 \ \text{Hz}; (b) 60,000 Hz\displaystyle \bold{(b)} \ 60,000 \ \text{Hz}.
 
A 1.20\displaystyle 1.20-kΩ\displaystyle \text{k}\Omega resistor and a 6.8\displaystyle 6.8-μF\displaystyle \mu\text{F} capacitor are connected in series to an ac source. Calculate the impedance of the circuit if the source frequency is (a) 60 Hz;\displaystyle \bold{(a)} \ 60 \ \text{Hz}; (b) 60,000 Hz\displaystyle \bold{(b)} \ 60,000 \ \text{Hz}.
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(a)\displaystyle \bold{(a)}

The reactance of the capacitor is:

XC=12πfC\displaystyle X_C = \frac{1}{2\pi f C}

The impedance is given by:

Z2=R2+XC2=R2+14π2f2C2\displaystyle Z^2 = R^2 + X^2_C = R^2 + \frac{1}{4\pi^2 f^2 C^2}

Then,

Z=12002+14π2602(6.8×106)2=1262 Ω\displaystyle Z = \sqrt{1200^2 + \frac{1}{4\pi^2 60^2 (6.8 \times 10^{-6})^2}} = \textcolor{blue}{1262 \ \Omega}
 
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