A generator produces a rectangular pulse train of period across a resistor of…

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 Alternating current: peak and rms values, the oscilloscope and rectification

Problem

A generator produces a rectangular pulse train of period

T

across a resistor of constant resistance

R = 50\;\Omega

. In each period the voltage is

V(t) = V_0

for

0 \le t < dT

and

V(t) = 0

for

dT \le t < T

, where the duty fraction

d

satisfies

0 < d \le 1

. The switching between the two levels is instantaneous. ((a)) By averaging

V^2

over one period, show that the root-mean-square voltage of this waveform is

V_{\mathrm{rms}} = V_0\sqrt{d}

, and check that it gives the expected result for

d = 1

. ((b)) Evaluate

V_{\mathrm{rms}}

for

V_0 = 12\;\mathrm{V}

and

d = 0.25

. ((c)) Find the mean value

\langle V\rangle

of the waveform for the same numbers. ((d)) Find the mean power dissipated in the

50\;\Omega

resistor.

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