Question

f =60Hz ww 15000 ele SH A Zuf capacitor is connected in series with a 1500 resistor, an 8 Hinductor, and a 60. He ac source. Calculate the impedance of the circuit. o 15k 2.0 KO 2.30 0 32 KO 8.0 kn MH 16 l tt | | | | | |

Answer 1

given data

frequency f = 60 Hz

capacitance C = 2 μF = 2x10^-6 F

Resistance R = 1500 Ω

Inductance L=8 H

We know that ꞷ = 2πf = (2)(3.142)(60) = 377 rad/s

we know that

inductive reactance X_L = ꞷL = (377)(8H) =3016 Ω

capacitive reactance X_C = 1/ꞷC = 1/(377)(2x10^-6 ) = 1,326.26 Ω

We know that series LCR circuit impedence is  

Z = ( R² + (X_L - X_C)² ) ^1/2

Plugging the values in the formula

Z = ((1500)² +(3016-1,326.26)²)^1/2 = 2259 Ω = 2.26 k Ω = approximately =2.30 k Ω

Z = 2.30 k Ω

ans is

impedence is  Z = 2.30 k Ω

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