a, b are standard formulas
c...add the reactances and resistances as complex numbers, then convert to polar form. Current=V/Z
c...add the reactances and resistances as complex numbers, then convert to polar form. Current=V/Z
1) Inductive Reactance (XL):
XL = 2 * ฯ * f * L
where:
ฯ โ 3.14159
f is the frequency in Hz
L is the inductance in Henrys
2) Capacitive Reactance (XC):
XC = 1 / (2 * ฯ * f * C)
where:
ฯ โ 3.14159
f is the frequency in Hz
C is the capacitance in Farads
3) Total Reactance (X):
X = XL - XC
4) Impedance (Z):
Z = โ(R^2 + X^2)
where:
R is the resistance in ohms
X is the total reactance
5) Current (I):
I = V / Z
where:
V is the voltage in RMS (Root Mean Square)
Now, let's calculate the values:
Given:
Resistance (R) = 50 ohms
Inductance (L) = 0.2 H
Capacitance (C) = 40 ฮผF = 40 * 10^(-6) F
Voltage (V) = 120 V
Frequency (f) = 60 Hz
Using the above formulas:
a) Inductive Reactance (XL):
XL = 2 * ฯ * f * L
= 2 * 3.14159 * 60 * 0.2
โ 75.398 ohms
b) Capacitive Reactance (XC):
XC = 1 / (2 * ฯ * f * C)
= 1 / (2 * 3.14159 * 60 * 40 * 10^(-6))
โ 66.548 ohms
c) Total Reactance (X):
X = XL - XC
= 75.398 - 66.548
โ 8.850 ohms
d) Impedance (Z):
Z = โ(R^2 + X^2)
= โ(50^2 + 8.850^2)
โ 51.193 ohms
e) Current (I):
I = V / Z
= 120 / 51.193
โ 2.348 A (Amps)
So, the answers are:
a) Inductive Reactance (XL) โ 75.398 ohms
b) Capacitive Reactance (XC) โ 66.548 ohms
c) Total Reactance (X) โ 8.850 ohms
d) Impedance (Z) โ 51.193 ohms
e) Current (I) โ 2.348 A (Amps)