# In series with a conductor with an active resistance of 1 kOhm, coils with an inductance of 0.5 gn

**In series with a conductor with an active resistance of 1 kOhm, coils with an inductance of 0.5 gn and a capacitor with a capacity of 1 microfarad are connected, determine the impedance of the alternating current circuit at a frequency of 10 kHz.**

The impedance of the AC circuit is determined by the formula

Z = √ (R ^ 2 + X ^ 2),

where R = 1 kOhm = 10 ^ 3 Ohm is the active resistance of the circuit; X is the reactance of the circuit, Ohm, determined by the formula

X = ω * L – 1 / (ω * C),

where L = 0.5 H is the inductance of the coil; C = 1 μF = 10 ^ (- 6) – capacitance of the capacitor; ω – cyclic vibration frequency, rad / s, which can be found by the formula

ω = 2 * π * ν,

where ν = 10 kHz = 10 ^ 4 Hz is the vibration frequency.

Substituting the presented expressions into the original formula, we get:

Z = √ {R ^ 2 + [2 * π * ν * L – 1 / (2 * π * ν * C)] ^ 2};

Z = √ {(10 ^ 3) ^ 2 + [2 * 3.14 * 10 ^ 4 * 0.5 – 1 / (2 * 3.14 * 10 ^ 4 * 10 ^ (- 6))] ^ 2 } = 31400 ohms = 31.4 k ohms.