For the test circuit shown in the figure derive an expression for the output vol

Question

For the test circuit shown in the figure derive an expression for the output voltage E_0 as a function of the input voltage E_i and the resistances shown for (a) the ideal case of the perfect voltmeter having R_m = infinity and (b) the non-ideal voltmeter case when R_m is finite. Show mathematically that the solution for case (b) becomes that for case (a) when R_m --> infinity.

For the test circuit shown in the figure derive an expression for the output voltage E_0 as a function of the input voltage E_i and the resistances shown for (a) the ideal case of the perfect voltmeter having R_m = infinity and (b) the non-ideal voltmeter case when R_m is finite. Show mathematically that the solution for case (b) becomes that for case (a) when R_m --> infinity.

Explanation / Answer

equivalent resistance = RmR2/(Rm+R2) + R1 + R3

current through E_0 = E_0/Req = I

so E0 = R2/R2+Rm * I

E0 = R2/R2+Rm * E_0/(RmR2/(Rm+R2) + R1 + R3)

when Rm--->infiity

E0 = zero

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