Two sinusoidal sources of the same angular frequency are connected in series

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electromagnetic induction and alternating-current circuits · Electromagnetic induction and alternating-current circuits

Electricity, Magnetism and Electromagnetism, Ch AC circuits: phasors, complex impedance, resonance and power

Problem

Two sinusoidal sources of the same angular frequency ω=2.0×103 rad s−1\omega = 2.0\times10^{3}\ \mathrm{rad\,s^{-1}} are connected in series, driving the same way round the loop, with an ideal resistor R=120 ΩR = 120\,\Omega and an ideal inductor L=40 mHL = 40\ \mathrm{mH}. The sources have zero internal impedance and the wires have zero resistance. Their voltages arev1=4.0cos⁡ωt V,v2=3.0cos⁡(ωt+60∘) V,v_1 = 4.0\cos\omega t\ \mathrm{V},\qquad v_2 = 3.0\cos(\omega t + 60^\circ)\ \mathrm{V},all phases being measured against cos⁡ωt\cos\omega t. ((a)) Add the two source voltages as phasors and write the total in the form V0cos⁡(ωt+ϕ)V_0\cos(\omega t + \phi): give V0V_0 and ϕ\phi. ((b)) Find the magnitude and the argument of the impedance ZZ of the series RR-LL pair at this angular frequency.

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