An ideal source is connected through a resistor to a node ; from a resistor runs to ground

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electronics, Instrumentation & Communication · Circuit foundations and passive networks

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

Problem

An ideal

10\,\mathrm{V}

source is connected through a resistor

R_1 = 20\,\mathrm{k\Omega}

to a node

A

; from

A

a resistor

R_2 = 20\,\mathrm{k\Omega}

runs to ground, and a capacitor

C = 0.5\,\mathrm{\mu F}

(initially uncharged) is also connected from

A

to ground. A switch in series with the source closes at

t = 0

. ((a)) Using the Thevenin equivalent of the source and the two resistors as seen by the capacitor, state

V_{\rm th}

R_{\rm th}

and the time constant

\tau

v_A(t)

for

t \ge 0

. ((b)) To observe the charging trace, a voltmeter of input resistance

R_m = 20\,\mathrm{k\Omega}

is connected from

A

to ground for the whole transient (it is present from

t=0

). Find the new Thevenin voltage

V_{\rm th}'

and resistance

R_{\rm th}'

that the capacitor now sees, and the new time constant

\tau'

. ((c)) With the meter connected throughout, at what time after the switch closes does the meter reading reach 63 per cent of its (meter-loaded) final value, and what voltage is that?

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