Previous Year Questions- A.C. Bridges

Q1: A balanced Wheatstone bridge ABCD has the following arm resistances:
R_AB = 1kΩ ± 2.1 is an unknown resistance; R_DA = 300Ω ± 0.4. The value of R_CD and its accuracy is   (2022)
(a) 30Ω ± 3Ω
(b) 30Ω ± 0.9Ω
(c) 3000Ω ± 90Ω
(d) $3000\Omega \pm 3\Omega$3000Ω ± 3Ω
Ans: (b)
Sol: The condition for balanced bridge
R_ABR_CD = R_DAR_BC
∴ R_CD = 30 ± 30 x (3/100) = 30 ± 0.9Ω

Q2: Inductance is measured by  (2021)
(a) Schering bridge
(b) Maxwell bridge
(c) Kelvin bridge
(d) Wien bridge
Ans: (b)
Sol: Maxwell's bridge is used for measurement of inductance.
Wein's bridge is used for measurement of frequency
Kelvin's bridge is used for measurement of low value of resistance.
Schering bridge is used for measurement of capacitance, dilectric loss and permittivity etc.

Q3: In the bridge circuit shown, the capacitors are loss free. At balance, the value of capacitance C₁ in microfarad is ______.  (SET-3 (2014))
(a) 0.1
(b) 0.2
(c) 0.3
(d) 0.4
Ans: (c)
Sol: Redrawing the given bridge circuit, we have:
Z₄ = 105 kΩ
At balance, current through galavanometer:
I_g = 0
and ∣Z₁∣∣Z₄∣ = ∣Z₂∣∣Z₃∣
= 0.3μF

Q4: The reading of the voltmeter (rms) in volts, for the circuit shown in the figure is _________   (SET-1 (2014))
(a) 80.32
(b) 141.42
(c) 160.45
(d) 180.78
Ans: (b)
Sol: Given bridge is shown in figure
From the given bridge circuit, we see that product of opposite arm impedance are equal
i.e. (-j) × (-j) = (j)(j)
or -1 = -1
Hence, the bridge is balanced, i.e. no current flows through the voltage source V.
v_i(t) = 100 sin ωt
Now, = (100/√2) Volt (rms value)
∴ Net current supplied by the source is
Z_eq = 0(i.e. net impedance of whole bridge = 0)
Current flow through each parallel path of the bridge circuit, therefore V = V_a - V_b
= -jI = -j141.42 volt (rms value)
∴ Reading of the voltmeter in volt (rms)
=V = V_ab = 141.42

Q5: Three moving iron type voltmeters are connected as shown below. Voltmeter readings are V, V₁ and V₂ as indicated. The correct relation among the voltmeter readings is   (2013)
(a)
(b) $V=V1+V2$V = V₁ + V₂
(c) V = V₁V₂  
(d) $V=V2-V1$V = V₂ - V₁ 
Ans: (d)
Sol: V₁ = -|j1Ω| x I
V₂ = -|j2Ω| x I
V = -j1Ω| x I + j2Ω| x I
= V₂ - V₁

Q6: The bridge method commonly used for finding mutual inductance is  (2012)
(a) Heaviside Campbell bridge
(b) Schering bridge
(c) De Sauty bridge
(d) Wien bridge
Ans: (a)
Sol: Heaciside Campbell bridge method is commonly used for finding mutual inductance.

Q7: A lossy capacitor C_x, rated for operation at 5 kV, 50 Hz is represented by an equivalent circuit with an ideal capacitor C_p in parallel with a resistor R_p. The value C_p is found to be 0.102 μF and value of R_p = 1.25MΩ. Then the power loss and tan δ of the lossy capacitor operating at the rated voltage, respectively, are  (2011)
(a) 10 W and 0.0002
(b) 10 W and 0.0025
(c) 20 W and 0.025
(d) 20 W and 0.04
Ans: (c)
Sol: C_P = 0.102 μF
R_P = 1.25 MΩ
Power loss =
= 20 W
tanδ  = RIX = (1/ωC_PR_P)
= 0.025

Q8: The bridge circuit shown in the figure below is used for the measurement of an unknown element Z_X. The bridge circuit is best suited when Z_X is a  (2011)
(a) low resistance
(b) high resistance
(c) low Q inductor
(d) lossy capacitor
Ans: (b)
Sol: The bridge is Maxwell bridge.
Element is an inductor.
Inductance = L_x effective resistance of the inductor = R_x
The bridge is limited to measurement of low Q inductor (1 < Q < 10).
It is clear from equation (i) that the measurement of high Q coils demands a large value of resistance R₁, perhaps 10⁵ or 10⁶Ω. The resistance boxes of such high value are very expensive. Thus for value of Q > 10, the bridge is unsuitable.
The bridge is also unsuited for coils with a very low value of Q(i.e. Q < 1).

Q9: The Maxwell's bridge shown in the figure is at balance. The parameters of the inductive coil are.  (2010)
(a) R = R₂R₃/R₄, L = C₄R₂R₃ 
(b) $L=R2R3/R4,R=C4R2R3$L = R₂R₃/R₄, R = C₄R₂R₃ 
(c) R = R₄/R₂R₃, L = C₄R₂R₃
(d) L = R₄/R₂R₃, R = 1/(C₄R₂R₃)
Ans: (a)
Sol: Z₁ = R + jωL
Z₂ = R₂
Z₃ = R₃
At balance,
Z₁Z₄ = Z₂Z₃
R₄(R + jωL) = R₂R₃(1 + jωC₄R₄)
RR₄ + jωLR₄ = R₂R₃ + jωR₂R₃R₄C₄
Equating real and imaginary terms
RR₄ = R₂R₃
ωLR₄ = ωR₂R₃R₄C₄
L = R₂R₃C₄

Q10: The ac bridge shown in the figure is used to measure the impedance Z.
 If the bridge is balanced for oscillator frequency f = 2 kHz, then the impedance Z will be  (2008)
(a) (260 + j0) ω
(b) (0 + j200) ω
(c) (260 - j200) ω
(d) (260 + j200)  ω
Ans: (a)
Sol: Z_AB = 500Ω
Z_CD = Z  
Z_BC = R_BC + (1/jωc)
Z_BC = 300 - j200Ω
Z_AD = RAD + jωL
Z_AD = 300 + j2π × 2 × 10³ × 15.91 × 10^-3
= 300 + j200Ω
At balance,
Z_AB × Z_CD = Z_BC × Z_AD
Z_CD = Z
Z = (260 + j0)Ω

Q11: A bridge circuit is shown in the figure below. Which one of the sequence given below is most suitable for balancing the bridge?  (2007)
(a) First adjust R₄, and then adjust R₁
(b) First adjust R₂, and then adjust R₃
(c) First adjust R₂, and then adjust R₄
(d) First adjust R₄, and then adjust R₂
Ans: (c)
Sol: z₁ = R₁ + jx₁ = R₁+jωL₁
z₂ = R₂
z₃ = R₃
z₄ = R₄ - jx₄ = R₄ -  (j/ωC₄)
Under balanced condition
z₁z₄ = z₂z₃
(R₁ + jωL₁)(R₄ - jx₄) = R₂R₃
Equating real and imaginary terms, we obtain
Solving above equations, we get
Q-factor of the coil Q =
Therefore, For a value of a greater than 10, the term (1/Q)² will be smaller than 1/1000 and can be neglected. Therefore equation (i) and (ii) reduces to
L₁ = R₂R₃C₄ ...(iii)
R₁ = ω²R₂R₃R₄C²₄ ...(iv)
R₄ appears only in equation (iv) and R₂ appears in both equation (iii) and (iv).
So first R₂ is adjusted and then R₄ is adjusted.

Q12: The items in Group-I represent the various types of measurements to be made with a reasonable accuracy using a suitable bridge. The items in Group-II represent the various bridges available for this purpose. Select the correct choice of the item in Group-II for the corresponding item in Group-I from the following  (2003)
(a) P = 2, Q = 3, R = 6, S = 5
(b) P = 2, Q = 6, R = 4, S = 5
(c) P = 2, Q = 3, R = 5, S = 4
(d) P = 1, Q = 3, R = 2, S = 6
Ans: (a)
Sol: Wheat stone bridge is used for measurement of medium resistance.
Kelvin double bridge is used for meserement of low resistance.
Schering bridge is used for meserement of low value of capacitances.
Wein's bridge is used for meserement of the frequency
Hay's bridge is used for meserement of inductance of a coil with a large time-constant.
Carey-foster bridge is used for comparision of resistances which are nearly equal.