A series RL circuit contains two resistors and two inductors. The resistors are 43 ? and 54 ?. The inductors have inductive reactances of 70 ? and 40 ?. The total impedance is _____.
Z=97+j110
in magnitude, Z=sqrt(97^2+110^2)=147ohms
To find the total impedance of the series RL circuit, we need to calculate the sum of the resistive and inductive components.
The total impedance (Z) can be calculated using the following formula:
Z = √(R² + (XL - XC)²)
Where:
R is the total resistance
XL is the sum of the inductive reactances
XC is the sum of the capacitive reactances
In this case, there are no capacitive components, so XC is zero.
R = 43 Ω + 54 Ω = 97 Ω
XL = 70 Ω + 40 Ω = 110 Ω
Now we can calculate the total impedance:
Z = √(97² + (110 - 0)²) ≈ √(9409 + 12100) ≈ √21509
Thus, the total impedance of the series RL circuit is approximately 146.6 Ω (rounded to one decimal place).
To find the total impedance of a series RL circuit, you need to calculate the equivalent impedance. The impedance (Z) of a resistor (R) is given by its resistance value, and the impedance (Z) of an inductor (L) is given by its inductive reactance (XL), which is a function of the angular frequency (w) and inductance (L).
The formula to calculate the impedance of a resistor is Z = R.
The formula to calculate the impedance of an inductor is Z = XL = wL.
The total impedance (Ztotal) of the series RL circuit is found by adding up the individual impedances:
Ztotal = Z1 + Z2 + Z3 + Z4 + ...
In this case, you have two resistors with values 43 ? and 54 ?, and two inductors with inductive reactances of 70 ? and 40 ?.
First, let's calculate the impedance of the resistors:
Z_resistor1 = 43 ?
Z_resistor2 = 54 ?
Now, let's calculate the impedance of the inductors:
Z_inductor1 = 70 ?
Z_inductor2 = 40 ?
Finally, add up the individual impedances to find the total impedance:
Ztotal = Z_resistor1 + Z_resistor2 + Z_inductor1 + Z_inductor2
Ztotal = 43 ? + 54 ? + 70 ? + 40 ?
Now, calculate the sum:
Ztotal = 207 ?
Therefore, the total impedance of the series RL circuit is 207 ?.