Properties of Bridge Circuits MCQ Quiz in বাংলা - Objective Question with Answer for Properties of Bridge Circuits - বিনামূল্যে ডাউনলোড করুন [PDF]
Last updated on Mar 23, 2025
Latest Properties of Bridge Circuits MCQ Objective Questions
Top Properties of Bridge Circuits MCQ Objective Questions
Properties of Bridge Circuits Question 1:
In the AC bridge, shown in the figure R = 103 Ω and C = 10-7 F. If the bridge is balanced at a frequency ω0, the value of ω0 in rad/s is-
Answer (Detailed Solution Below) 10000
Properties of Bridge Circuits Question 1 Detailed Solution
At balance condition,
Z1 Z4 = Z2 Z3
\(\Rightarrow R\left[ {R + \frac{1}{{j\omega c}}} \right] = 2R\;\left[ {\frac{{R\left( {\frac{1}{{j\omega c}}} \right)}}{{R + \frac{1}{{j\omega c}}}}} \right]\)
\(\Rightarrow R\left[ {R + \frac{1}{{j\omega c}}} \right] = 2R\;\left[ {\frac{R}{{1 + jR\omega c}}} \right]\)
\(\Rightarrow \left[ {R + \frac{1}{{j\omega c}}} \right]\left[ {1 + j\omega RC} \right] = 2R\)
\(\Rightarrow \left( {R + R} \right) + \frac{1}{{j\omega c}} + j\omega {R^2}c = 2R\)
\(\Rightarrow j\omega {R^2}C = \frac{{ - 1}}{{j\omega c}}\)
\(\Rightarrow {\omega ^2}{R^2}{C^2} = 1 \Rightarrow \omega = \frac{1}{{RC}} = \frac{1}{{{{10}^3} \times {{10}^{ - 7}}}} = 10000\;rad/s\)
Properties of Bridge Circuits Question 2:
For the bridge shown Z1 = 200 ∠20° Ω, Z2 = 150 ∠30° Ω and Z3 = 300 ∠-30° Ω. What is the value of Z4 so that the bridge is balanced?
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 2 Detailed Solution
At bridge balance condition,
Z1 Z4 = Z2 Z3
⇒ 200 ∠20° Z4 = 150 ∠30° 300 ∠-30°
⇒ Z4 = 225 ∠-20° ΩProperties of Bridge Circuits Question 3:
The impedance of a basic ac bridge arms are ZAB = 300 Ω, ZBC = 150 Ω ∠60°, ZCD = 400 Ω/30° ZDA = unknown if ω = 1000 radian/s, the components of the unknown arms has the resistance 692.82 in
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 3 Detailed Solution
For bridge balance:
ZAB × ZCD = ZBC × ZAD
300 × 400 ∠30° = ZAD × 150 ∠60°
800 ∠30° = ZAD ∠60°
ZAD = 692.82 – j 400
Capacitive reactance \({x_c} = \frac{1}{{wc}}\)
\(C = \frac{1}{{400 \times 1000}} = 2.5\mu F\)
Properties of Bridge Circuits Question 4:
In the AC bridge shown in figure R = 105 Ω and C = 10-8 F. If the bridge is balanced at a frequency ωo, the value of ω0 in rad/sec is _______.
Answer (Detailed Solution Below) 1000
Properties of Bridge Circuits Question 4 Detailed Solution
\(R \times \left( {R + \frac{1}{{j\omega C}}} \right) = 2R \times \frac{R}{{1 + j\omega RC}}\)
\(\frac{{1 + j\omega RC}}{{j\omega RC}} = \frac{{2R}}{{1 + j\omega RC}}\)
(1 + jωRC)2 = jωR2C
1 + 2jωRC – ω2R2C2 = jωR2C
Equate real part
1 – ω2R2C2 = 0
\({\omega ^2} = \frac{1}{{{R^2}{C^2}}}\)
\(\omega = \frac{1}{{RC}}\)
Now put value of R and C
\(\omega = \frac{1}{{{{10}^6} \times {{10}^{ - 8}}}} = {10^3}rad/sec\)
Properties of Bridge Circuits Question 5:
The a.c. bridge in figure remains balance if z comprises of
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 5 Detailed Solution
At bridge balance condition,
\(\begin{array}{l} ({R_1})\left( {\frac{1}{{j\omega {C_1}}}} \right) = z\left( {\;{R_2} + \frac{1}{{j\omega {C_2}}}} \right)\\ z = \frac{{({R_1})\left( {\frac{1}{{j\omega {C_1}}}} \right)}}{{\left( {\;{R_2} + \frac{1}{{j\omega {C_2}}}} \right)}} \end{array}\)
It is equivalent to a resistor and a capacitor are connected in parallel.Properties of Bridge Circuits Question 6:
Find the excitation frequency (in Hz) in the Ac Bridge shown in figure under balance condition. The circuit component values are given as
R1 = 100 kΩ,
R3 = R4 = 100 kΩ,
C1 = 2 C2 = 10 nF
Answer (Detailed Solution Below) 158 - 160
Properties of Bridge Circuits Question 6 Detailed Solution
under bridge balance condition,
\(\left[ {{R_1} + \frac{1}{{j\omega {c_1}}}} \right]{R_4} = {R_3}\left[ {\frac{{{R_2}\left( {\frac{1}{{j\omega {c_2}}}} \right)}}{{{R_2} + \frac{1}{{j\omega {c_2}}}}}} \right]\)
Given that, \({R_3} = {R_4}\)
\(\left[ {{R_1} + \frac{1}{{j\omega {c_1}}}} \right] = \left[ {\frac{{{R_2}\left( {\frac{1}{{j\omega {c_2}}}} \right)}}{{{R_2} + \frac{1}{{j\omega {c_2}}}}}} \right]\)
\(\left[ {{R_1} + \frac{1}{{j\omega {c_1}}}} \right] = \left[ {\frac{{{R_2}}}{{{R_2}j\omega {c_2} + 1}}} \right]\)
\(\begin{array}{l} \frac{{\left( {{R_{1\;}}j\omega {c_1} + 1} \right)}}{{j\omega {c_1}}} = \frac{{{R_2}}}{{j{R_2}\omega {c_2} + 1}}\\ \left( {1 + \;j\omega {R_1}{C_1}} \right)\left( {1 + \;j\omega {R_2}{C_2}} \right) = j\omega {C_1}{R_2}\\ 1 + \;j\omega {R_1}{C_1} + \;j\omega {R_2}{C_2} - {\omega ^2}{R_1}{R_2}{C_1}{C_2} = \;j\omega {C_1}{R_2} \end{array}\)
By comparing real parts on both sides,
\(\begin{array}{l} 1 - {\omega ^2}{R_1}{R_2}{C_1}{C_2} = 0\\ \omega = \frac{1}{{\sqrt {{R_1}{R_2}{C_1}{C_2}} }} \end{array}\)
By comparing imaginary parts on both sides,
\(\begin{array}{l} {R_1}{C_1} + {R_2}{C_2} = {C_1}{R_2}\\ {R_2} = \left( {{C_1} - {C_2}} \right) = {R_1}{C_1}\\ {R_2} = \frac{{{R_1}{C_1}}}{{\left( {{C_1} - {C_2}} \right)}} = \frac{{100 \times {{10}^3} \times 10 \times {{10}^{ - 9}}}}{{\left( {10 \times {{10}^{ - 9}} - 5 \times {{10}^{ - 9}}} \right)}}\\ = 200\:k\Omega \;\\ f = \frac{1}{{2 \pi \sqrt {{R_1}{R_2}{C_1}{C_2}} }}\\ =\frac{1}{{2\pi \sqrt {100 \times {{10}^3} \times 200 \times {{10}^3} \times 10 \times {{10}^{ - 9}} \times 5 \times {{10}^{ - 9}}} }} \end{array}\)
= 159.15 HzProperties of Bridge Circuits Question 7:
The bridge circuit in figure is balanced. The magnitude of current I is
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 7 Detailed Solution
At bridge balance condition,
\(\begin{array}{l} {V_A} = {V_B}\\ {V_A} = {V_S}\left( {\frac{4}{{1 + 4}}} \right) = \frac{{4{V_S}}}{5}\\ {V_B} = {V_S} - 2\\ \frac{{4{V_S}}}{5} = {V_S} - 2\\ 4{V_S} = 5{V_S} - 10\\ {V_S} = 10V\\ I = \frac{{{V_S}}}{{5 \times {{10}^3}}} + \frac{{{V_S} - 2}}{{2 \times {{10}^3}}}\\ I = \frac{{10}}{{5 \times {{10}^3}}} + \frac{8}{{2 \times {{10}^3}}}\\ I = 6\;mA \end{array}\)
Properties of Bridge Circuits Question 8:
The impedances of a basic ac bridge arms are
ZAB = 250 Ω
ZBC = 100 ∠60° Ω
ZCD = 400 ∠30° Ω
ZDA = Unknown
If ω = 1000 radian/sec, the components of the unknown arm has the resistance 500√3 Ω isAnswer (Detailed Solution Below)
Properties of Bridge Circuits Question 8 Detailed Solution
At bridge balance condition,
\(\frac{{{Z_{AB}}}}{{{Z_{DA}}}} = \frac{{{Z_{BC}}}}{{{Z_{CD}}}}\)
\(\frac{{250}}{{{Z_{DA}}}} = \frac{{100\angle 60}}{{400\angle 30}}\)
\({Z_{DA}} = \frac{{250 \times 400\angle 30}}{{100\angle 60}}\)
\({Z_{DA}} = 1000\angle - 30\)
\(= \left( {1000 \times \frac{{\sqrt 3 }}{2} - j\;500} \right){\rm{\Omega }}\)
\({Z_{DA}} = \left( {500 \times \sqrt 3 - j\;500} \right)\)
Negative sign of reactance value indicates that, it is capacitive reactance.
\({X_c} = 500\)
\(\frac{1}{{\omega C}} = 500\)
\(C = \frac{1}{{\left( {500} \right)\left( {1000} \right)}} = 2 \times {10^{ - 6}}F = 2\mu F\)
Hence ZDA is a resistance of 500√3 Ω in series with a capacitor of 2 μF
Properties of Bridge Circuits Question 9:
If the given circuit is a balanced bridge, what should be in place of ‘X’ ?
Answer (Detailed Solution Below)
Properties of Bridge Circuits Question 9 Detailed Solution
For balanced bridge, Z1Z4 = Z2Z3
\(X{R_4} = \left( {{R_2} - \frac{J}{{\omega {C_2}}}} \right){R_3}\)
\(X = \frac{{{R_2}{R_3}}}{{{R_4}}} - J\frac{1}{{\frac{{\omega {C_2}{R_4}}}{{{R_3}}}}}\)
X = resistance and capacitance in series.Properties of Bridge Circuits Question 10:
For the given circuit, if the current through branch BD is zero what is the value of battery current I in mA upto two decimal places?
Answer (Detailed Solution Below) 42.8 - 43.0
Properties of Bridge Circuits Question 10 Detailed Solution
If current through BD is zero, then the bridge is balanced.
For balanced bridge, R × 75 = 150 × 100
R = 200 Ω
Equivalent resistance of the circuit, Req = 350 || 175
= 116.67 Ω
\(I = \frac{5}{{116.67}} = 0.04286A = 42.86mA\)