An ideal source feeds a divider of (from the source to the junction) and (junction to…

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Electronics for Measurement, Ch The resistive network: two laws, one equivalent and the loading error

Problem

An ideal

12.0\,\mathrm{V}

source feeds a divider of

R_1 = 8.0\,\mathrm{k}\Omega

(from the source to the junction) and

R_2 = 8.0\,\mathrm{k}\Omega

(junction to ground). A data-logger of input resistance

R_{\rm m} = 40\,\mathrm{k}\Omega

is connected from the junction to ground. Treat every source and resistor as ideal and steady. ((a)) Write the current-law equation at the junction with the logger connected and solve for the junction voltage

v

. ((b)) Remove the logger and reduce the divider to its Thevenin equivalent: state

V_{\rm th}

and

R_{\rm th}

, each found from an open-circuit and a short-circuit test. ((c)) Use the Thevenin equivalent to predict the reading with the logger reconnected, and check it against part (a). ((d)) What minimum input resistance would the logger need for the reading to be within one per cent of

V_{\rm th}

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