COMPLEX NOTATION ; A voltage, v = 150sin(314t + 30�) volts, is maintai...
Complex Notation for Voltage
The given voltage, v = 150sin(314t + 30°) volts can be represented in complex notation as:
V = 150∠30°
Calculating Current Phasor
We know that the impedance of a circuit containing only resistance and inductance is given by:
Z = R + jωL
where R is the resistance, L is the inductance, and ω is the angular frequency given by:
ω = 2πf
where f is the frequency of the voltage.
Substituting the values of R, L, and ω, we get:
Z = 20 + j31.4
The current phasor can be calculated using Ohm's law:
I = V/Z
Substituting the values of V and Z, we get:
I = (150∠30°)/(20 + j31.4) = 5.3∠-24.9° A
R.M.S. Values in Rectangular Notation
The r.m.s. value of the voltage can be calculated using the formula:
Vrms = Vmax/√2
Substituting the value of Vmax, we get:
Vrms = 150/√2 = 106.1 volts
The r.m.s. value of the current can be calculated using the formula:
Irms = Imax/√2
where Imax is the maximum value of the current phasor.
Substituting the value of Imax, we get:
Irms = 5.3/√2 = 3.75 A
Therefore, the r.m.s. values of the voltage and current phasors in rectangular notation are:
V = 106.1 + j0 volts
I = 3.75 - j2.78 A
R.M.S. Values in Polar Notation
The r.m.s. values of the voltage and current phasors in polar notation can be calculated using the formula:
Vrms = |V|
Irms = |I|
where |V| and |I| are the magnitudes of the voltage and current phasors, respectively.
Therefore, the r.m.s. values of the voltage and current phasors in polar notation are:
|V| = 106.1 volts
|I| = 4.59 A
The angle of the current phasor can be calculated as:
θ = tan-1(Im/Re)
where Im and Re are the imaginary and real parts of the current phasor, respectively.
Substituting the values of Im and Re, we get:
θ