The Ammeter and the Voltmeter — Question 9

Question 9

A series ohmmeter reads parallel return paths as part of the unknown

A simple ohmmeter contains an ideal battery E, total internal series resistance Rs and a current movement. Its shorted-terminal current is I0. An unpowered specimen Rx remains connected in parallel with another passive resistance Rp.

1. Derive the resistance indicated from current I and explain which equivalent resistance it represents.

2. For Rx=1.00 kilohm and Rp=3.00 kilohm, find the indicated value and its fractional difference from Rx.

Question 9 - Solution

A series ohmmeter reads parallel return paths as part of the unknown

(a) Method and calculation

$$I_0=E/R_s,\quad I=E/(R_s+R_{\mathrm{eq}}).$$$$R_{\mathrm{indicated}}=R_s(I_0/I-1)=R_{\mathrm{eq}}=R_x\parallel R_p.$$

(b) Interpretation and further calculation

$$R_{\mathrm{indicated}}=\frac{(1.00)(3.00)}{1.00+3.00}=.750\,\mathrm{k\Omega}.$$$$\frac{R_{\mathrm{indicated}}-R_x}{R_x}=-.250=-25.0\%.$$

Physical check

The ohmmeter responds to every conducting path between its terminals; it cannot identify which path belongs to the specimen.