An ideal resistor is in series with an ideal capacitor across a source of frequency

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

R = 220\,\Omega

is in series with an ideal capacitor

C = 0.47\ \mu\mathrm{F}

across a source

V(t) = 10\cos\omega t\ \mathrm{V}

of frequency

f = 500\ \mathrm{Hz}

, with

\omega = 2\pi f

. The wires have zero resistance and only the steady sinusoidal response is wanted. Phases are measured against

\cos\omega t

. ((a)) Give the impedance

Z

of the pair in Cartesian form: its real part and its imaginary part, in ohms. ((b)) Find

|Z|

and the angle by which the current leads the applied voltage. ((c)) Find the current amplitude in mA.

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