E1C06 09/14/2010
11:55:8 Page 254
R eq
equivalent resistance (V)
R m
meter resistance (V)
dR
change in resistance (V)
T m
torque on a current carrying loop in a
magnetic field ml
2
t
À2
À
Á
a
angle
t
time constant (t)
F(f)
phase shift at frequency f
u
angle
PROBLEMS
6.1 Determine the maximum torque on a current loop having 20 turns, a cross-sectional area of 1 in.
2 , and
experiencing a current of 20 mA. The magnetic field strength is 0.4 Wb/m
2 .
6.2 A 10-V voltage is applied across a Wheatstone bridge of Figure 6.13 to measure the value of a
variable resistance sensor R 1 . Arms are fixed at R 2 ¼ R 4 ¼ 250 V. Variable resistance arm 3 is
adjusted to R 3 ¼ 300 V to achieve a condition of zero current through the galvanometer. What is the
value of R 1 ? Should we be concerned about loading error? Explain or estimate.
6.3 Determine the loading error as a percentage of the output for the voltage dividing circuit of
Figure 6.15, if R T ¼ R 1 þ R 2 and R 1 ¼ kR T . The parameters of the circuit are
R T ¼ 500 V; E i ¼ 10 V; R m ¼ 10;000 V; k ¼ 0:5
What would be the loading error if expressed as a percentage of the full-scale output? Show that the
two answers for the loading error are equal when expressed in volts.
6.4 Consider the Wheatstone bridge shown in Figure 6.13. Suppose
R 3 ¼ R 4 ¼ 200 V
R 2 ¼ variable calibrated resistor
R 1 ¼ transducer resistance ¼ 40x þ 100
a. When x ¼ 0, what is the value of R 2 required to balance the bridge?
b. If the bridge is operated in a balanced condition in order to measure x, determine the relationship
between R 2 and x.
6.5 For the voltage-dividing circuit of Figure 6.15, develop and plot the family of solutions for
loading error versus r ¼ R 1 =ðR 1 þ R 2 Þ as a function of ðR 1 þ R 2 Þ=R m . Under what conditions
will the loading error in measuring the open circuit potential E o be less than 7% of the input
voltage?
6.6 For the Wheatstone bridge shown in Figure 6.13, R 1 is a sensor whose resistance is related to a
measured variable x by the equation R 1 ¼ 20 x
2 . If R 3 ¼ R 4 ¼ 100 V and the bridge is balanced when
R 2 ¼ 46 V, determine x.
6.7 A force sensor has as its output a change in resistance. The sensor forms one leg (R 1 ) of a basic
Wheatstone bridge. The sensor resistance with no force load is 500 V, and its static sensitivity is
0.5 V/N. Each arm of the bridge is initially 500 V
a. Determine the bridge output for applied loads of 100, 200, and 350 N. The bridge is operated as a
deflection bridge, with an input voltage of 10 V.
b. Determine the current flow through the sensor.
c. Repeat parts a and b with R m ¼ 10 kV and R s ¼ 600 V.
254 Chapter 6 Analog Electrical Devices and Measurements
11:55:8 Page 254
R eq
equivalent resistance (V)
R m
meter resistance (V)
dR
change in resistance (V)
T m
torque on a current carrying loop in a
magnetic field ml
2
t
À2
À
Á
a
angle
t
time constant (t)
F(f)
phase shift at frequency f
u
angle
PROBLEMS
6.1 Determine the maximum torque on a current loop having 20 turns, a cross-sectional area of 1 in.
2 , and
experiencing a current of 20 mA. The magnetic field strength is 0.4 Wb/m
2 .
6.2 A 10-V voltage is applied across a Wheatstone bridge of Figure 6.13 to measure the value of a
variable resistance sensor R 1 . Arms are fixed at R 2 ¼ R 4 ¼ 250 V. Variable resistance arm 3 is
adjusted to R 3 ¼ 300 V to achieve a condition of zero current through the galvanometer. What is the
value of R 1 ? Should we be concerned about loading error? Explain or estimate.
6.3 Determine the loading error as a percentage of the output for the voltage dividing circuit of
Figure 6.15, if R T ¼ R 1 þ R 2 and R 1 ¼ kR T . The parameters of the circuit are
R T ¼ 500 V; E i ¼ 10 V; R m ¼ 10;000 V; k ¼ 0:5
What would be the loading error if expressed as a percentage of the full-scale output? Show that the
two answers for the loading error are equal when expressed in volts.
6.4 Consider the Wheatstone bridge shown in Figure 6.13. Suppose
R 3 ¼ R 4 ¼ 200 V
R 2 ¼ variable calibrated resistor
R 1 ¼ transducer resistance ¼ 40x þ 100
a. When x ¼ 0, what is the value of R 2 required to balance the bridge?
b. If the bridge is operated in a balanced condition in order to measure x, determine the relationship
between R 2 and x.
6.5 For the voltage-dividing circuit of Figure 6.15, develop and plot the family of solutions for
loading error versus r ¼ R 1 =ðR 1 þ R 2 Þ as a function of ðR 1 þ R 2 Þ=R m . Under what conditions
will the loading error in measuring the open circuit potential E o be less than 7% of the input
voltage?
6.6 For the Wheatstone bridge shown in Figure 6.13, R 1 is a sensor whose resistance is related to a
measured variable x by the equation R 1 ¼ 20 x
2 . If R 3 ¼ R 4 ¼ 100 V and the bridge is balanced when
R 2 ¼ 46 V, determine x.
6.7 A force sensor has as its output a change in resistance. The sensor forms one leg (R 1 ) of a basic
Wheatstone bridge. The sensor resistance with no force load is 500 V, and its static sensitivity is
0.5 V/N. Each arm of the bridge is initially 500 V
a. Determine the bridge output for applied loads of 100, 200, and 350 N. The bridge is operated as a
deflection bridge, with an input voltage of 10 V.
b. Determine the current flow through the sensor.
c. Repeat parts a and b with R m ¼ 10 kV and R s ¼ 600 V.
254 Chapter 6 Analog Electrical Devices and Measurements