Anonymous
Anonymous asked in Science & MathematicsEngineering · 7 years ago

# Suppose a resistor of 10 ohms, a capacitor of 820 pF, and a coil of 10 microHenry are in parallel. The frequen?

Suppose a resistor of 10 ohms, a capacitor of 820 pF, and a coil of 10 microHenry are in parallel. The frequency is 1MHz. What is the complex impedance?

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There are (3) devices here of which (2) are frequency dependant; the capacitor and the inductor.

The capacative reactance Xc = 1 / (2 * pi * Freq * C ) = 1 / (2 * pi * 10E6 * 820E-12) = 194.0914 ohms or -j194.0914 as a phasor.

The inductive reactance XL = 2 * pi * Freq * L = 2 * pi * 10E6 * 10E-7 = 62.8319 ohms or +j62.8319 as a phasor.

Since the phasors add -j194.0914 to +j62.8319 = -j131.2595

The total complex impedance is the sum of the frequency dependant components and the non-frequency dependant components (e.g. resistor), so the final answer is

10 -j131.2595

This has an total impedance of 131.6399 ohms with a phasor angle of -85.6433 degrees.

Notice that the angle is negative showing the dominance of the negative capacitive (lagging) reactance over the positive (leading) inductive reactance.

Source(s): ALOT of engineering experience.