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Chapter 11: Problem 1

The impedance of a component is \(Z=12-12 \mathrm{j}\). State (a) the resistance, (b) the reactance, (c) the phase of the voltage relative to the current.

Short Answer

Expert verified
Answer: The resistance is 12 Ohms, the reactance is -12 Ohms (capacitive), and the phase difference between the voltage and current is -45 degrees (the voltage lags the current by 45 degrees).

Step by step solution

01

Calculate the Resistance

The resistance (R) can be taken as the real part of the complex impedance. Given that the impedance is Z = 12 - 12j, the resistance R = 12 Ohms.
02

Calculate the Reactance

The reactance (X) is the imaginary part of the complex impedance. Given that the impedance is Z = 12 - 12j, the reactance X = -12 Ohms. Note that the negative sign indicates that it is a capacitive reactance.
03

Determine Phase of Voltage Relative to Current

To find the phase (Φ) of the voltage relative to the current, we can calculate the angle between the impedance vector and the real axis of the complex plane. This can be done using the following formula: Φ = arctan(X/R), where X is the reactance and R is the resistance. Plugging in the values, we get Φ = arctan(-12/12) = arctan(-1) = -45 degrees. Thus, the phase difference between the voltage and current is -45 degrees, which implies that the voltage lags the current by 45 degrees.

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