1.4 METERS AND MEASUREMENTS 47
(ii) ForgR= 1 ,Req→∞. The internal controlled source provides all of the current
throughR, thereby reducing the input currentito be zero for a given value ofv.
(iii) ForgR= 2 ,Req=−R, which is a negative equivalent resistance. This means that
the controlled source provides more current than that going throughR; the current
direction ofiis reversed whenv>0. However, the relationv=Reqiis satisfied at
the input terminals.
1.4 Meters and Measurements
The subject of electrical measurements is such a large one that entire books have been written on
the topic. Only a few basic principles will be introduced here. Practical measurements are made
with real instruments, which in general disturb the operation of a circuit to some extent when they
are connected. Measurements may be affected bynoise, which is undesirable randomly varying
signals.
Voltmeter
In order to measure the potential difference between two terminals or nodes of a circuit, a voltmeter
is connectedacrossthese two points. A practical voltmeter can usually be modeled as a parallel
combination of an ideal voltmeter (through which no current flows) and a shunt resistanceRV,as
shown in Figure 1.4.1. The internal resistanceRVof an ideal voltmeter is infinite, while its value
in practice is of the order of several million ohms. There are what are known as dc voltmeters
and ac voltmeters. An ac voltmeter usually measures the rms value of the time-varying voltage.
Rv
−
+
−
+
Ideal
voltmeter
Practical voltmeter
Figure 1.4.1
EXAMPLE 1.4.1
An electromechanical voltmeter with internal resistance of 1 kand an electronic voltmeter with
internal resistance of 10 Mare used separately to measure the potential difference betweenA
and the ground of the circuit shown in Figure E1.4.1. Calculate the voltages that will be indicated
by each of the two instruments and the percentage error in each case.
Rv
−
+
−
+
Ground Voltmeter
2 V
10 kΩ
10 kΩ
A Figure E1.4.1
