A series RCL contains 150 ohm resistor, a 1.75x10^-6F capcitor and inductance of inductor 0.035H and voltage of generator 60.0 Hz. Determine its total impedance.
a) 1500 ohm
b) 1900 ohm
c) 1700 ohm
d) 500 ohm
e) 300 ohm
The angular frerquency is w = 2 pi f = 377 rad/s.
Total impedance is
Z = sqrt [R^2 + (wL - 1/(wC))^2]
= sqrt[150^2 + (13.2 - 1516)^2]
= sqrt[150^2 + 1503]^2] = 1510 ohms
a) is the closest to the correct answer. The capacitive reactance dominates.
To determine the total impedance of the series RCL circuit, we need to calculate the individual impedances of the resistor (R), capacitor (C), and inductor (L), and then add them together.
1. Resistor (R) impedance:
The impedance of a resistor in an AC circuit is given by its resistance (R) and is given as:
ZR = R
Given in the problem: R = 150 ohm
2. Capacitor (C) impedance:
The impedance of a capacitor in an AC circuit is given by the formula:
ZC = 1 / (2πfC)
Given in the problem: C = 1.75x10^-6F
Given in the problem: f = 60.0 Hz
Using the values, we can calculate the impedance of the capacitor:
ZC = 1 / (2π(60.0 Hz)(1.75x10^-6F))
3. Inductor (L) impedance:
The impedance of an inductor in an AC circuit is given by the formula:
ZL = 2πfL
Given in the problem: L = 0.035H
Given in the problem: f = 60.0 Hz
Using the values, we can calculate the impedance of the inductor:
ZL = 2π(60.0 Hz)(0.035H)
After calculating the values of ZR, ZC, and ZL, we can find the total impedance (Z) by adding them together:
Z = ZR + ZC + ZL
Once you have obtained Z, compare it to the options provided:
a) 1500 ohm
b) 1900 ohm
c) 1700 ohm
d) 500 ohm
e) 300 ohm
Select the option that matches the calculated value of Z.
Perform the calculations and select the correct answer from the given options.