- If E = 10 V 230° and IS = 5 A 210°, what is the total impedance ZT?
A) 32.1 Ω + j38.3 Ω
B) 0.47 Ω - j0.17 Ω
C) 1.88 Ω + j0.68 Ω
D) 38.3 Ω + j32.1 Ω

Question

- If E = 10 V 230° and IS = 5 A 210°, what is the total impedance ZT?
A) 32.1 Ω + j38.3 Ω 
B) 0.47 Ω - j0.17 Ω 
C) 1.88 Ω + j0.68 Ω 
D) 38.3 Ω + j32.1 Ω

Quizplus · Accepted Answer

To find the total impedance $Z_T$, we use Ohm's Law in its phasor form, $Z = \frac{E}{I}$. Given $E = 10\angle230^\circ$ V and $I_S = 5\angle210^\circ$ A, we first convert them to rectangular form. $E = 10(\cos230^\circ + j\sin230^\circ) = -6.43 - j7.66$ V, and $I_S = 5(\cos210^\circ + j\sin210^\circ) = -4.33 - j2.5$ A. Then, $Z_T = \frac{-6.43 - j7.66}{-4.33 - j2.5} = 1.88 + j0.68$ Ω.