A series RL circuit contains two resistors and two inductors. The resistors are 33 W and 47 W. The inductors have inductive reactances of 60 W and 30 W. Angle theta is _____.
To find the angle theta in a series RL circuit, we need to consider the values of the inductive reactances and the resistors.
In a series RL circuit, the total impedance is given by the formula:
Z = √(R^2 + (XL - XC)^2)
Where:
XL = inductive reactance
XC = capacitive reactance (which is 0 in this case since it's a series RL circuit)
Given:
Resistor 1 (R1) = 33 Ω
Resistor 2 (R2) = 47 Ω
Inductive Reactance 1 (XL1) = 60 Ω
Inductive Reactance 2 (XL2) = 30 Ω
The total resistance is given by:
RTotal = R1 + R2 = 33 Ω + 47 Ω = 80 Ω
To find the total inductive reactance (XLTotal):
XLTotal = XL1 + XL2 = 60 Ω + 30 Ω = 90 Ω
Now, we can calculate the impedance using the formula:
Z = √(R^2 + (XL - XC)^2)
Z = √(80^2 + (90 - 0)^2)
Z = √(6400 + 8100)
Z = √14500
Z ≈ 120.42 Ω
The angle theta can then be calculated using the formula:
θ = arctan(XLTotal / RTotal)
θ = arctan(90 Ω / 80 Ω)
θ ≈ 47.59 degrees
Therefore, the angle theta is approximately 47.59 degrees.
To find the angle theta in a series RL circuit, we need to calculate the total impedance of the circuit and then find the arctangent of the ratio of the total inductive reactance to the total resistance.
First, let's calculate the total impedance (Z) of the circuit. In a series circuit, the impedance is the sum of the resistive and inductive components.
Z = R + jX
where R is the total resistance and X is the total inductive reactance.
Given that the resistors are 33 Ω and 47 Ω, and the inductive reactances are 60 Ω and 30 Ω, we can calculate the total resistance and total inductive reactance:
Total resistance (Rtotal) = 33 Ω + 47 Ω = 80 Ω
Total inductive reactance (Xtotal) = 60 Ω + 30 Ω = 90 Ω
Now, we can calculate the total impedance:
Z = Rtotal + jXtotal
= 80 Ω + j90 Ω
The impedance is a complex number, with the real part representing the resistance and the imaginary part representing the reactance.
Finally, to find the angle theta, we take the arctangent of the ratio of the total inductive reactance to the total resistance:
θ = arctan(Xtotal / Rtotal)
= arctan(90 Ω / 80 Ω)
Calculating this using a calculator or trigonometric table, we find:
θ ≈ 48.37 degrees
Therefore, the angle theta is approximately 48.37 degrees.
Resistance and reactance are usually measured in Ohms, but
Well, tanθ = 90/80, so ...