An ideal resistor and an ideal inductor are joined in series across a sinusoidal…

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

An ideal resistor and an ideal inductor are joined in series across a sinusoidal source of angular frequency

\omega

. The connecting wires have zero resistance, and the source has been running long enough that only the steady sinusoidal response remains. In that steady state the current amplitude is

50\,\mathrm{mA}

, the voltage across the resistor is

v_R = 5.0\cos\omega t\ \mathrm{V}

and the voltage across the inductor is

v_L = 12\cos(\omega t + 90^\circ)\ \mathrm{V}

. All phases are measured against

\cos\omega t

. ((a)) Add the two element voltages as phasors and write the source voltage in the form

V_0\cos(\omega t + \phi)

: give

V_0

and

\phi

. ((b)) Find the magnitude

|Z|

of the total impedance of the series pair.

Browse the problem library