# The resistance depends on the frequency

## Big Bang 7, textbook

Fundamentals of electrical engineering 27 RG 7.1 G 7.1 Competence area electrodynamics 9 case, the connected devices always represent a mixture of all three resistances. Fig. 27.23: Summary overview of possible courses of the power curve: a) pure ohmic resistance, d) pure reactance, b + c) Mixture The real power that can be used to generate other forms of energy and that ultimately has to be paid in the electricity bill depends on the phase shift between voltage and current strength (Fig. 27.23). This means that the zero crossing does not occur at the same time. The unused power is lost when the electric and magnetic fields build up. Info: Incandescent filament coil Info: Electric motor -> p. 10 Incandescent filament coil The filament of a light bulb (Fig. 27.24) is a coil and therefore also has an inductive resistance. How big is it? Let's do an estimate. We initially assume that the incandescent lamp (200W) is a purely ohmic resistor. The following applies: U eff = I eff · R and P = U eff · I eff, which means that R is around 265Ω. Now we calculate R L. We assume that the helix is 3 cm long and has a radius of 0.1 mm. The inductance (Section 26.6, "Big Bang 6") of the coil is therefore L = (µ 0 · N 2 · A) / l ≈ 10 –8 H and the inductive resistance (ω l) is thus 3.3 · 10 - 6 Ω. This is around a factor of 10 8 smaller than R and therefore absolutely negligible. Heating coils such as those found in stoves, irons or kettles are practically pure ohmic resistors. i Fig. 27.24: The double filament of a 200 W bulb: It has 90 large turns - we neglect the small turns. Formula: Inductive resistance RL = ω LRL… inductive resistance [Ω] ω… angular frequency (= 2 π f) [s –1] L… inductance of the coil [H] Fig. 27.21: With an inductive resistance, the current lags behind the voltage . The power required to build up the magnetic field is returned in the next phase. In a capacitor, the current leads the voltage by a quarter of a period (Fig. 27.22). This is due to the fact that a voltage can only be built up in the capacitor as the charge increases, and this requires a previous flow of current. The capacitive resistance is indirectly proportional to the frequency of the alternating current and to the capacitance of the capacitor (for the derivation of the equation, see F19, p. 13). Formula: Capacitive resistance RC = 1 ___ ω CRC… capacitive resistance [Ω] ω… angular frequency (= 2 π f) [s –1] C… capacitance of the capacitor [F] Fig. 27.22: With a capacitive resistance, the current rushes the Excitement ahead. The power that is necessary for charging is returned when discharging. With purely inductive or capacitive resistance, the mean power is zero because the positive and negative areas cancel each other out. In connection with coil and capacitor, one speaks of reactances and reactive power. If you were to connect a giant capacitor to the grid, it wouldn't cost any money, but it would still put a strain on the grid during the charging phase. That's why you shouldn't do that - you don't get any of it anyway. In real F F For testing purposes only - property of the publisher öbv

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