The Ammeter and the Voltmeter — Question 6

Question 6

A voltmeter outside the ammeter includes the instrument voltage burden

An ideal voltmeter spans the series combination of an unknown resistor R and an ammeter of resistance RA=2.00 ohm. The ammeter reads .200 A and the voltmeter reads 10.0 V.

1. Find R and the power actually dissipated in the specimen.

2. Derive the fractional overestimate produced by V/I and compare its useful resistance range with the arrangement that places the voltmeter only across R.

Question 6 - Solution

A voltmeter outside the ammeter includes the instrument voltage burden

(a) Method and calculation

$$V=I(R+R_A)\Rightarrow R=V/I-R_A=50-2=48.0\,\Omega.$$$$P_R=I^2R=(.200)^2(48)=1.92\,\mathrm W.$$

(b) Interpretation and further calculation

$$R_{\mathrm{naive}}=R+R_A,\quad\frac{R_{\mathrm{naive}}-R}{R}=R_A/R.$$$$R\gg R_A\text{ favors this layout; }R\ll R_V\text{ favors the specimen-only voltage layout}.$$

Physical check

The measured product VI includes ammeter heating as well as specimen heating.