The Ammeter and the Voltmeter — Question 4

Question 4

A finite voltmeter measures a loaded source rather than its open-circuit emf

A source has open-circuit voltage 15.0 V and Thevenin resistance 30.0 kilohm. A voltmeter of resistance RV=120 kilohm is connected across its output.

1. Find the reading, meter current and percentage loading error.

2. Find the minimum RV needed for a loading error no greater than two percent.

Question 4 - Solution

A finite voltmeter measures a loaded source rather than its open-circuit emf

(a) Method and calculation

$$V_m=15\frac{120}{30+120}=12.0\,\mathrm V,\quad I_m=12/(120000)=100\,\mathrm{\mu A}.$$$$\epsilon=1-V_m/15=30/(30+120)=.200=20.0\%.$$

(b) Interpretation and further calculation

$$\epsilon=\frac{R_{\mathrm{th}}}{R_{\mathrm{th}}+R_V}\le.0200.$$$$R_V\ge R_{\mathrm{th}}(.0200^{-1}-1)=1.47\,\mathrm{M\Omega}.$$

Physical check

An ideal voltmeter is the limit of infinite input resistance, not zero input resistance.