Solve the Problem $Z$ Can Be Calculated Using the Equation $$\frac { 1 } { Z } = \left( \frac { 1 } { Z _ { 1 } } + \frac { 1 } { Z _ { 2 } } \right)$$

question 177

Multiple Choice

Solve the problem.
-In a parallel electrical circuit, the impedance $Z$ can be calculated using the equation
$$\frac { 1 } { Z } = \left( \frac { 1 } { Z _ { 1 } } + \frac { 1 } { Z _ { 2 } } \right)$$
where $\mathrm { Z } _ { 1 }$ and $\mathrm { Z } _ { 2 }$ are the impedances for the branches of the circuit. The phase angle measures the phase difference between the voltage and the current in an electrical circuit. If the impedance $\mathrm { Z }$ is expressed in the form $a + b i , \theta$ can be determined by the equation $\tan \theta = b / a$ . Determine the phase angle $\theta$ (in degrees) for a parallel circuit in which $\mathrm { Z } _ { 1 } = 10 + 20 \mathrm { i }$ and $\mathrm { Z } _ { 2 } = 30 + 10 \mathrm { i }$ .

• A) \(60 ^ { \circ }\)
• B) \(30 ^ { \circ }\)
• C) \(45 ^ { \circ }\)
• D) \(0 ^ { \circ }\)

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