Çözüldü Alternating Circuit Analysis - Pythagorean Theorem

Circuit elements having pure resistance, inductance, and capacitance are connected in series to an AC source. If a voltmeter reads 40 volts when connected across the resistor, 50 volts across the inductor, and 20 volts across the capacitor, what would be the voltmeter reading when it is connected across all three at once?

A) 900·√5
B) 50
C) √70
D) √110
E) 100·√5

Using the Pythagorean theorem for the phasor combination of the resistive and net reactive components:
[ 40^2 + (50 - 20)^2 ]^0.5 = (1600 + 900)^0.5 = √2500 = 50 volts.

What is the effective value of a sinusoidal electromotive force e(t) = 100·sin(ω·t) + (100 / 3)·sin(2ω·t - π / 2) ?

e(t) = 100·sin(ω·t) - (100 / 3)·cos(2ω·t)
E = [ 100^2 + (-100 / 3)^2 ]^0.5 / √2 = 100·(1 + 1 / 9)^0.5 / √2 = (100 / 3)·√(10 / 2) = (100 / 3)·√5 volts.

Source (Turkish): "Elektroteknik - III", Prof.Dr. Adnan Ergeneli, İDMMA Yayınları, Sayı: 93 / 1, 1975, Sayfa 18, Problem 29.4, Yanıtlar Sayfa 283