AC Bridge
1. Using the balanced AC bridge as shown below, find the constant of
Zx as R and C or L considered as series circuit.
4. The similar-angle bridge as shown below is balanced with the
following conditions: Z1 =2000 Ω∠0 ; Z2 =15000 Ω∠ 0 ;
Z3 =1000 Ω∠−50. Find the constant Rx and Cx.
2. Using the balanced ac bridge as shown below with the following
condition, Z1 =100 Ω∠ 0 ; Z2 =300 Ω∠−40 ; Z3 =100 Ω∠−20 ;
find the constant of Zx.
5. Given the Maxwell bridge as shown below, find the equivalentseries resistance and inductance of Rx and Lx, at balance.
3. Given the similar-angle bridge as shown below, find the equivalentseries values of Rx and Cx at balance.
6. The Maxwell bridge as shown below is balanced with the following
conditions: : Z1 =153.8 Ω∠−75; Z2 =100 Ω∠0 ; Z3 =1000 Ω∠0
. Find the constant Rx and Lx.
7. The opposite-angle bridge as shown below, find the equivalent
series resistance and inductance (Rx and Lx) at balance
8. The opposite-angle bridge as shown below is balanced when
Z1 =1500 Ω∠−50; R2=200 Ω∠ 0; R3=200 Ω∠0 . Find the
constant Rx and Lx.
9. Given the Wein bridge as shown below, find the series-equivalent
resistance and capacitance of R4 and C4 at balance, when Z3 equals
11. Refer to the balanced radio-frequency bridge as shown below
having the Zx terminals short-circuited. When the unknown
impedance is inserted across the Zx terminals and the bridge is
rebalanced, capacitor C’1 now equals 1.1 µF. find the unknown
equivalent series constant of Rx and Lx or Cx.
7790 ∠−72.8
12. The radio-frequency shown below is balanced and Zx is shorted
with the following result conditions: Z1 =( 120− j159 ) Ω ;
Z2 =− j 1592 Ω; Z3 =10 Ω; Z 4=( 100− j 132.6 ) Ω. the unknown
10. In the Wein bridge as shown below, find the constant of the parallel
arms of R3 and C3 for the following conditions: Z1 =100000 Ω∠0 ;
R2=25000 Ω∠ 0; R3=1050 Ω∠−17.7
impedance is connected across across the Zx terminals and the
bridge is rebalanced with the following conditions:
Z1 =( 120− j144.7 ) Ω ; Z2 =− j 1592 Ω; Z3 =10 Ω;
Z 4=( 100− j 144.7 ) Ω. find the equivalent-series elements for the
unknown impedance.
15. A simple capacitance bridge, as shown below, uses a 0.1 µF
standard capacitor and two standard resistors each of which is
adjustable from 1 kΩ to 200 kΩ. Determine the minimum and
maximum capacitance values that can be measured on the bridge.
13. The Schering bridge as shown below is operated at balance. Find the
equivalent-series resistance and capacitance of Rx and Cx.
16.
A. A series-resistance capacitance bridge as shown below, has a 1
kHz supply frequency. The bridge components at balance are C1 =
0.1 µF, R1 = 109.5 Ω, R3 = 1 kΩ, and R4 = 2.1 kΩ. calculate the
resistive and capacitive components of the measured capacitor, and
determine the capacitor dissipation factor.
14. The balanced Schering bridge below has the following conditions:
Z1 =( 2588.2− j 9659.3 ) Ω ; Z2 =10000 Ω; Z3 =− j 159000 Ω; Find
the constant of Rx and Cx.
B. Calculate the parallel equivalent circuit components (Cp and Rp)
for the measured capacitor. Also determine the value of R1 and R4
required to balance Cp and Rp when the bridge is operated as a
parallel-resistance capacitor bridge. Assume that R3 remains 1 kΩ.
17. A parallel-resistance capacitance bridge shown below uses 0.1 µF
capacitor C1, and the supply frequency is 1 kHz. At balance, R1 =
547 Ω, R3 = 1 kΩ, and R4 = 666 Ω. Determine the parallel RC
components of the measured capacitor, and calculate the capacitor
dissipation factor.
18. An inductance comparison bridge has L1 = 100 µH and R4 = 10 kΩ.
when measuring an unknown inductance, null is detected with R1 =
37.1 Ω and R3 = 27.93 kΩ. the supply frequency is 1 MHz. calculate
the measured inductance and its resistive component. Also,
determine the Q factor of the inductor.
19. An inductor with a marked value of 100 mH and a Q of 21 at 1 kHz is
to be measured on a Maxwell bridge. The bridge uses a 0.1 µF
standard capacitor and a 1 kΩ standard resistor for R1. Calculate the
resistance values of R3 and R4 at which balance is likely to be
achieved.
20. A Maxwell bridge with a 10 kHz supply has a 0.1 µF standard
capacitor and a 100 Ω standard resistor for R1. Resistor R3 and R4
can each be adjusted from 100 Ω to 1 kΩ. calculate the range of
inductances and Q factors that can be measured on the bridge.
21. A. A hay bridge with a 500 Hz supply frequency has C3 = 0.5 µF and
R4 = 900 Ω. If balance is achieved when R1 = 466 Ω and R3 = 46.1 Ω,
calculate the inductance, resistance, and Q factor of the measured
inductor.
B. calculate the series equivalent circuit components L X and RX for
the Lp and Rp quantities. Also determine the resistance R 1 and R3
required to balance LX and RX, when the circuit components are
connected as a Maxwell bridge. Assume that R 4 and C3 remain 900 Ω
and 0.5 µF, respectively.
22. A balance AC bridge has the following constants. Arm AB ( R = 1kΩ
in parallel with C = 0.047 µF ), Arm BC ( R= 2kΩ in series with C =
0.047 µF ) Arm CD ( unknown) Arm DA ( C = 0.25 µF). the frequency
of the oscillator is 1 kHz. Determine the constant of arm CD.
23. A bridge is balanced at a frequency of 1 kHz and has the following
components. Arm AB (C = 0.02 µF pure capacitor ), Arm BC ( R=
500Ω pure resistance ) Arm CD ( unknown) Arm DA ( R = 600Ω in
parallel with C = 0.1 µF). Derive the balance condition and find the
constant of arm CD, considered as series circuit.
24. A 1000 Hz bridge has the following constants Arm AB ( R = 1kΩ in
parallel with C = 0.025 µF ), Arm BC ( R= 1kΩ in series with C = 0.25
µF ) Arm CD ( L = 50 mH in series with R = 200 Ω ) Arm DA ( unknown
). Find the constant of arm DA to balance the bridge. Express the
result as pure R in series with a pure C or L, and as a pure R in
parallel with pure C or L.
25. An ac bridge has the following constants. Arm AB ( C = 0.2 µF pure
capacitor ), Arm BC ( R= 500Ω pure resistance ) Arm CD ( a series
combination of R = 50 Ω and L = 0.1 H ) Arm DA ( C = 0.5 µF in series
with a resistance RS.) if ω = 2000 rad / s.
a. Find RS to obtain bridge balance.
b. Can complete balance be obtained by adjustment of R S? If
not, specify the position and value of an adjustable
resistance to complete the balance.
26. A Maxwell – Wein bridge consists of the following: Arm AB having
resistance value of 1.2 kΩ in parallel with a capacitor of 1 µF, Arm
BC having resistance value of 500 Ω, Arm AD having resistance value
of 300 Ω, Arm BD having resistance and inductance in series.
Determine the value of the unknown inductance.
27. An Anderson’s bridge consists of the following: Arm AD having
resistance value of 500 Ω, Arm CD having a resistance of 1000 Ω,
Arm ED having a resistance of 600 Ω, Arm EC having a capacitor of
0.5 µF, Arm BC having resistance value of 300 Ω, Arm AB having
resistance and inductance in series. Determine the value of the
unknown inductance.
28. A Owen’s bridge consist of the following: Arm AB having capacitor
of 0.5 µF, Arm BC having resistance value of 600 Ω, Arm AD having
resistance value of 300 Ω in series with a capacitor 0.75 µF, Arm BD
having resistance and inductance is series. Determine the value of
the unknown resistance and unknown inductance.
29. A De Sauty bridge consists of the following: Arm AB having a
resistance of 1 kΩ, Arm BC having a capacitor value of 0.75 µF, Arm
AD having resistance value of 300 Ω, Arm BD having unknown
capacitor. Determine the value of the unknown capacitor.