Vin=10cos(1000t) V drives the shown 3 kΩ resistor in series with a parallel 1 kΩ–1 μF branch. Find input-impedance magnitude in kΩ to one decimal place.
At ω=1000 rad/s, capacitor impedance is −j1000 Ω. In parallel with 1000 Ω, its equivalent is 1000/(1+j)=500−j500 Ω. Adding the series resistor yields 3500−j500 Ω. Magnitude is √(3500²+500²)≈3535.5 Ω=3.5 kΩ to one decimal, B.
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