If a circuit has impedance Z = 10 + j30 Ω and supply voltage V = 230 V, what is the current magnitude?

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Prepare for the 3rd Year Electrical Trades Qualification (TQ) exam. Use flashcards and multiple choice questions to master the material. Each question comes with hints and explanations to help you succeed. Get set for your qualification!

Multiple Choice

If a circuit has impedance Z = 10 + j30 Ω and supply voltage V = 230 V, what is the current magnitude?

Explanation:
In AC circuits, the current is found using Ohm’s law with impedance: I = V / Z, where Z is a complex number. To get the current magnitude, you divide the voltage magnitude by the impedance magnitude. For Z = 10 + j30, the impedance magnitude is sqrt(10^2 + 30^2) = sqrt(1000) ≈ 31.62 Ω. With V = 230 V (RMS), the current magnitude is 230 / 31.62 ≈ 7.28 A, which rounds to about 7.3 A. The phase angle is arctan(30/10) ≈ 71.6°, so the current lags the voltage by roughly 71.6 degrees.

In AC circuits, the current is found using Ohm’s law with impedance: I = V / Z, where Z is a complex number. To get the current magnitude, you divide the voltage magnitude by the impedance magnitude.

For Z = 10 + j30, the impedance magnitude is sqrt(10^2 + 30^2) = sqrt(1000) ≈ 31.62 Ω. With V = 230 V (RMS), the current magnitude is 230 / 31.62 ≈ 7.28 A, which rounds to about 7.3 A.

The phase angle is arctan(30/10) ≈ 71.6°, so the current lags the voltage by roughly 71.6 degrees.

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