Question

You have a 170 Ω resistor, a 0.800 h inductor, and a 6.40 μf capacitor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has a voltage amplitude of 28.0 V and an angular frequency of 210 rad/s. What is the impedance of the circuit?

Answer 1

The impedance of the series circuit containing a 170 Ω resistor and a 0.800 H inductor with an angular frequency of 210 rad/s is approximately 239 Ω.

Step-by-step explanation:

To calculate the impedance of a series circuit with a resistor (R) and an inductor (L) at a given angular frequency (ω), we use the formula Z = sqrt(R^2 + (X_L - X_C)^2), where Z is the impedance, X_L is the inductive reactance, and X_C is the capacitive reactance. In this case, since there is no capacitor in the circuit, X_C is 0.

The inductive reactance is given by X_L = ωL, where L is the inductance. For the provided values, the reactance of the inductor at the given angular frequency is X_L = 210 rad/s * 0.800 H = 168 Ω. The total impedance of the circuit would then be Z = sqrt(170^2 + 168^2) = sqrt(28900 + 28224) Ω = sqrt(57124) Ω ≈ 239 Ω.