A timer circuit for a slow-blink indicator switches an ideal source directly onto a…

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

Electronics for Measurement, Ch Capacitors, inductors and the time constant

Problem

A timer circuit for a slow-blink indicator switches an ideal

9.0\,\mathrm{V}

source directly onto a resistor

R

in series with a capacitor

C

that starts completely uncharged. A threshold comparator fires when the capacitor voltage reaches 90 per cent of the supply voltage, and the design calls for this to happen between

18\,\mathrm{ms}

and

22\,\mathrm{ms}

after the switch closes. You may use

t_{90} = \tau\ln 10

for the time at which an RC step response reaches 90 per cent of its final value. Standard E12 preferred values are

1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2

and their decades. ((a)) Find the range of time constants

\tau

that meets the

18

–

22\,\mathrm{ms}

specification. ((b)) Take

C = 2.2\,\mathrm{\mu F}

, an E12 preferred value. Find the range of

R

that keeps

\tau = RC

inside the range from part (a), and choose the nearest E12 preferred resistor value lying inside that range. ((c)) State the initial capacitor voltage, the final capacitor voltage, and the time constant that follow from your chosen

R

and

C

, and use the initial-value/final-value method to write

v_C(t)

without resolving the differential equation. ((d)) Check that the comparator trips inside the specified window by computing

t_{90}

for your chosen component values.

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