At the phasor voltage measured by an ideal (infinite-impedance) oscilloscope probe…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electronics, Instrumentation & Communication · Foundations of mathematical language

Electronics for Measurement, Ch Phasors, impedance and the frequency response

Problem

At f=1.00 kHzf = 1.00\,\mathrm{kHz} the phasor voltage measured by an ideal (infinite-impedance) oscilloscope probe across a component is V‾=(3−4j) V\underline{V} = (3 - 4j)\,\mathrm{V} (peak volts). A technician reasons: "the real part, 3 V3\,\mathrm{V}, is what the scope shows at t=0t=0; the imaginary part, −4 V-4\,\mathrm{V}, must be the voltage the scope shows a quarter cycle later, since multiplying by jj rotates a phasor by 90∘90^\circ." ((a)) Write the true instantaneous voltage v(t)v(t) in the form Vpkcos⁡(ωt+ϕ)V_{\rm pk}\cos(\omega t + \phi). ((b)) Evaluate v(t)v(t) at t=T/4t = T/4 (a quarter cycle after t=0t=0, T=1/fT=1/f) and compare it with the technician's claim of −4 V-4\,\mathrm{V}.

Browse the problem library