**Measurement of Inductance and Capacitance ( ****Electrical Measurements ****) MCQs – ****Electrical Measurements ****MCQs**

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**Electrical Measurements MCQs – Measurement of Inductance and Capacitance ( Electrical Measurements ) MCQs**

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# Schering Bridge

**1. Schering bridge is one of the most widely used AC bridges.****a) True**

b) False**Answer: a****Explanation: Schering bridge is an AC bridge used for the measurement of unknown capacitance, dielectric loss and power factor. It is one of the most commonly used AC bridges.**

**2. Schering bridge is used for _________**

a) low voltages only**b) low and high voltages**

c) high voltages only

d) intermediate voltages only**Answer: b****Explanation: Schering bridge is used for both low as well as high voltages. A particular bridge connection is used for low voltage. High voltages employ the use of a different type of Schering bridge.**

**3. Power factor of a Schering bridge is _________**

a) p.f. = sin∅_{x} = ^{Zx}⁄_{Rx}

b) p.f. = cot∅_{x} = ^{Rx}⁄_{Zx}**c) p.f. = cos∅ _{x} = ^{Rx}⁄_{Zx}**

d) p.f. = tan∅

_{x}=

^{Rx}⁄

_{Zx}

**Answer: c**

**Explanation: The power factor of the RC combination in a Schering bridge is given by the relation p.f. = cos∅x =**

^{Rx}⁄Zx .**where,**

**Rx is the series resistance**

**Zx is the series impedance comprising of Rx and Cx.**

**4. For phase angles close to 90°, the power factor of the bridge is _________**

a) p.f. = ωR_{x}

b) p.f. = ωC_{x}

c) p.f. = R_{x} C_{x}**d) p.f. = ωR _{x} C_{x}Answer: d**

**Explanation: When phase angle reaches 90°, reactance equals the impedance and the power factor of the bridge is calculated using the relation,**

**5. For a series RC circuit, what is δ?****a) voltage between series RC combination and C**

b) voltage between series RC combination

c) voltage across C

d) voltage across R**Answer: a****Explanation: In a series RC circuit, δ refers to the angle between the series combination of R _{x}, C_{x} and the voltage across the capacitance C_{x}. δ is also known as the loss angle.**

**6. What is the expression for the loss angle?**

a) tan δ = ωR_{4}**b) tan δ = ωR _{4} C_{4}**

c) tan δ = ωC

_{4}

d) tan δ = R

_{4}C

_{4}

**Answer: b**

**Explanation: The expression for the loss angle can be computed as the ratio of the tangent of the voltage drop across resistance R**

_{x}to the voltage drop across the capacitance C_{x}.**7. Quality factor is given by which of the following expression?**

a) Q = ^{1}⁄_{R}

b) Q = R**c) Q = ^{X}⁄_{R}**

d) Q = XR

**Answer: c**

**Explanation: The quality factor the Schering bridge circuit is defined as Q =**

^{X}⁄_{R}.**where, X =**

^{1}⁄_{wC}is the capacitive impedance.**8. Dissipation factor is the reciprocal of quality factor.****a) True**

b) False**Answer: a****Explanation: Dissipation factor for a circuit is defined as the reciprocal of the quality factor.****It is given by the expression Q = ^{1}⁄_{wCR}. It basically provides information about the quality of a capacitor.**

**9. Commercial Schering bridge can be used for the measurement of capacitances from _____________**

a) 10pF to 0.1nF**b) 100pF to 1μF**

c) 50nF to 10mF

d) 25mF to 5F**Answer: b****Explanation: Commercial Schering bridges are used for the measurement of capacitances in the range of a few pico farads to a few micro farads. Accuracy varies in the range of –2% to +2%.**

**10. A Schering bridge can be used for the ______________**

a) measuring voltages

b) measuring currents**c) testing capacitors**

d) protecting the circuit from temperature rises**Answer: c****Explanation: A Schering bridge can be used with both low voltage as well as high voltages. A Schering bridge is basically used for the measurement of small capacitances at low voltages with high precision.**

**High Voltage Schering Bridge**

**1. A Schering bridge can be used for capacitance measurements at low voltages.**

a) True**b) False****Answer: b****Explanation: When a Schering bridge is used for the measurement of small capacitances at low voltages, it comprises of errors. In order to avoid this a high voltage Schering bridge is used.**

**2. How is the high voltage obtained?****a) by using a step up transformer**

b) by using a high voltage source

c) by using a step down transformer

d) by using a high current source**Answer: a****Explanation: High voltage supply for a Schering bridge is obtained by making use of a step up transformer. The frequency for the high voltage supply used in a Schering bridge is 50 Hz.**

**3. The detector used in a high voltage Schering bridge is _________**

a) tunable circuit

b) e.m.f source**c) vibration galvanometer**

d) headphone**Answer: c****Explanation: A high voltage Schering bridge is used for the measurement of low capacitance values at high voltages. A vibration galvanometer is used as a detector in a high voltage Schering bridge.**

**4. Detector is very sensitive in a high voltage Schering bridge.****a) True**

b) False**Answer: a****Explanation: In a high voltage Schering bridge the ratio arms have high impedance values. As a result, a very small current is drawn by the ratio arms. Hence the detector must be very sensitive in a high voltage Schering bridge.**

**5. How are the inter-capacitance errors minimized?**

a) by separating the plates of the capacitance**b) by using earthing**

c) by reducing the area of cross section of the capacitors

d) by increasing the distance between the capacitor plates**Answer: b****Explanation: In a high voltage Schering bridge, errors due to inter-capacitance between the high and low impedance ratio arms can be eliminated through earthing screens.**

**6. How to minimize the effect of earth capacitance?**

a) by increasing the supply voltage

b) by using a series resistance**c) by using a Wagner ground connection**

d) by using an inductor across the circuit**Answer: c****Explanation: In a high voltage Schering bridge, the effect of earth capacitance on the circuit including the galvanometer and the contact leads is minimized by making use of a Wagner ground connection.**

**7. What is the effect of breakdown of high voltage capacitor?**

a) No effect

b) voltage drop across the circuit reduces

c) circuit components rupture**d) a high voltage appears across the branches****Answer: d****Explanation: In a high voltage Schering bridge, a very high voltage appears across the branches when the breakdown of high voltage capacitor occurs. This is prevented by making use of a spark gap across the branches involved.**

**8. What is the dependence of frequency on the balance equation?****a) independent**

b) varies by a factor of 2

c) depends on the supply magnitude

d) depends on the detector used**Answer: a****Explanation: In a high voltage Schering bridge, the balance equation does not depend on the frequency of operation of the circuit. A detector is only used for detecting the balance condition in a bridge circuit.**

**Maxwell’s Inductance Capacitance Bridge**

**1. Maxwell inductance capacitance bridge can be used for _________****a) measurement of inductance**

b) measurement of capacitance and inductance

c) measurement of resistance

d) measurement of voltage and current**Answer: a****Explanation: A Maxwell inductance capacitance bridge is used for the measurement of inductance by making comparison with a standard capacitance value. Voltmeter is used to measure voltage, while an ammeter is used to measure current.**

**2. Balance equation for computing the unknown resistance is?**

a) R_{x} = R2R1**b) R _{x} = R2R3R1**

c) R

_{x}= R3R1

d) R

_{x}= 1R1

**Answer: b**

**Explanation: The balance condition for determining the value of the unknown resistance is given by the relation R**

_{x}= R2R3R1**where, R**

_{1}and R_{3}are variable resistances and R_{2}is a fixed resistance.**3. Balance equation for computing the value of the unknown inductance is?**

a) L_{x} = R_{2} R_{3}

b) L_{x} = R_{2} C_{1}**c) L _{x} = R_{2} R_{3} C_{1}**

d) L

_{x}= R

_{3}C

_{1}

**Answer: c**

**Explanation: The balance equation for determining the value of the unknown inductance is given by the relation Lx= R2 R3 C1.**

**where,**

**C1 is the capacitance across the resistance R1**

**R3 is a variable resistance and R2 is a fixed resistance.**

**4. Quality factor of the circuit is given by _________**

a) Q = ωC_{1}

b) Q = ωR_{1}

c) Q = ω**d) Q = ωR _{1} C_{1}Answer: d**

Explanation: The quality factor of a Maxwell inductance capacitance bridge is given by the relation_{}

**5. Standard inductor requires no shielding.**

a) True**b) False****Answer: b****Explanation: Stray magnetic fields are present in a circuit consisting of inductances and capacitances. In order to eliminate the stray magnetic fields proper shielding is required for the standard inductance.**

Measurement Of Inductance And Capacitance MCQs

**6. Standard inductor provides rated inductance directly.**

a) True**b) False****Answer: b****Explanation: When the current flow through the standard inductance is adjusted precisely, it provides its rated value of inductance.**

**7. What is the significance of capacitors in a Maxwell bridge?**

a) they are used to block dc

b) they are used to block ac**c) they are cheap**

d) they are expensive**Answer: c****Explanation: In a Maxwell inductance capacitance bridge, the capacitors are cheaper when compared to a stable and accurate standard value of inductors.**

**8. The bridge balance equation can be written in _________**

a) impedance form

b) resistance form

c) conductance form**d) admittance form****Answer: d****Explanation: The bridge balance equation for a Maxwell inductance capacitance bridge consists of admittances. This is due to the connection of capacitance in parallel across the resistance in one of the ratio arms.**

**Advantages and Limitations of Maxwell Bridge**

**1. What is the significance of the balance equation on losses?****a) independent of losses in inductance**

b) independent of losses in capacitance

c) independent of losses in resistance

d) independent of losses in the circuit**Answer: a****Explanation: The balance equation in a Maxwell inductance capacitance bridge is independent of the losses associated with an inductance. According to the balance equation the unknown inductance is computed as L _{x} = R_{2} R_{3} C_{1}.**

**2. Balance equation is dependent on frequency.**

a) True**b) False****Answer: b****Explanation: The balance equation in a Maxwell inductance capacitance bridge is independent on the measurement of frequency. The balance equation does not contain frequency terms such as ω and as a result, it is independent of frequency.**

**3. How can R _{1} be scaled?**

a) by using a scale

**b) by using an ohmmeter**

c) by calibration

d) by using a galvanometer

**Answer: c**

**Explanation: The resistance R**

_{1}in a Maxwell inductance capacitance bridge can be scaled through calibration. The value of the Quality factor Q can be read directly through calibration.**4. Scale of resistance can be calibrated.****a) True**

b) False**Answer: a****Explanation: The resistance R _{1} in a Maxwell inductance capacitance bridge can be calibrated directly. As a result the value of the unknown inductance can be read directly.**

**5. Bridge can be used for the measurement of _________**

a) high Q values

b) intermediate Q values

c) very low Q values**d) low Q values****Answer: d****Explanation: A Maxwell inductance capacitance bridge can be used for the measurement of low Q values only of the order of 1 to 10. This is because at high Q factor values the angular balance condition is not satisfied.**

**6. The balance condition is _________**

a) is easy to obtain**b) is difficult to obtain**

c) can’t be obtained

d) exists always**Answer: b****Explanation: The balance condition in a Maxwell inductance capacitance bridge is difficult to obtain. This occurs due to an interaction between resistance and reactance components in the bridge circuit.**

**7. Commercial Maxwell bridges measures _________****a) inductances in the range of 1 to 1000H**

b) capacitances in the range of 10mF to 1F

c) resistances in the range of 0.001 Ω to 1Ω

d) power in the range of 1W to 50MF**Answer: a****Explanation: Basically a Maxwell bridge is used for the measurement of inductance in terms of known standard capacitance value. Inductances in the range of 1 to 1000H with an accuracy range of ±2% can be measured.**

**8. At high Q values, the angular balance condition is _________**

a) satisfied**b) not satisfied**

c) independent of Q factor

d) partially affected**Answer: b****Explanation: For high Q factor values in a Maxwell inductance capacitance bridge, the angular balance condition is affected. The relation θ _{1} + θ_{4} = θ_{2} + θ_{3} is not satisfied at high Q factor values. This occurs as θ_{4} reaches 90°. θ_{1} must become –90° as per the angular balance condition. But for this the value of R_{1} should be very high, which is not practically feasible.**

**Shielding and Grounding of Bridges**

**1. In general bridges consist of __________****a) lumped inductances**

b) lumped resistances

c) distributed capacitance

d) distributed impedance**Answer: a****Explanation: AC bridges in general such as Maxwell, Anderson, Schering, etc consist of lumped components such as inductance.**

**2. Stray capacitance exists between the components.****a) True**

b) False**Answer: a****Explanation: In general in AC bridges, stray capacitance exists between the components of the bridge with respect to the ground. These stray capacitances short the ratio arms and lead to errors in the measurement.**

**3. The magnitude of stray capacitances is fixed.**

a) True**b) False****Answer: b****Explanation: Stray capacitances are uncertain in nature. Their magnitude depends on the adjustment of the bridge arms and the position of the operator.**

**4. Stray capacitance effects can be minimized by __________**

a) making use of an inductance

b) connecting a resistance in series**c) shielding and grounding**

d) using a galvanometer**Answer: c****Explanation: The stray capacitance effects in an AC bridge can be eliminated by shielding and grounding. This method helps in making the stray capacitances constant in value. They can be compensated.**

**5. Most popular method of avoiding the stray capacitance effects is __________**

a) by grounding

b) by using guard rings

c) by using galvanometer**d) by using Wagner device****Answer: d****Explanation: A Wagner earthing device is used in general to eliminate the stray capacitance effects in AC bridges. The stray capacitance effects between the components in the ratio arms with respect to ground can be eliminated through this method.**

**6. Wagner device is a ____________****a) capacitance bridge**

b) resistance bridge

c) inductance bridge

d) impedance bridge**Answer: a****Explanation: A Wagner earth device is generally used for shielding and grounding purpose. It consists of capacitances in the ratio arms along with a series RC combination connected across the ends of the bridge forming a potential divider.**

**7. Which is the guarding arm?**

a) parallel RC combination**b) series RC combination**

c) resistance R

d) capacitance C**Answer: b****Explanation: The series combination of R and C in a Wagner earth device forms a potential divider across the ratio arms. It is also known as the guard arm.**

**8. Bridge is suitable for _________**

a) coils with high Q values**b) coils with low Q values**

c) coils with intermediate Q values

d) coils with very high Q values**Answer: b****Explanation: The Maxwell inductance capacitance bridge is basically used for the measurement of quality factor (Q) of inductance coils with low Q values.**

**Advanced Problems on Measurement of Inductance using AC Bridges**

**1. In the Owen’s bridge shown in below figure, Z _{1} = 200∠60°, Z_{2} = 400∠-90°, Z_{3} = 300∠0°, Z_{4} = 400∠30°. Then the _______**

a) Bridge is balanced with given impedance values

b) Bridge can be balanced, if Z

_{4}= 600∠60°

c) Bridge can be balanced, if Z

_{3}= 400∠0°

**d) Bridge cannot be balanced with the given configuration**

**Answer: d**

**Explanation: For Bridge to be balanced, the product of impedances of the opposite arm should be equal in magnitude as well as phase angle. Here Z**

_{3}Z_{2}≠ Z_{1}Z_{4}for whatever chosen value. Therefore the Bridge cannot be balanced.**2. In Maxwell’s capacitance bridge for calculating unknown inductance, the various values at balance are, R _{1} = 300 Ω, R_{2} = 700 Ω, R_{3} = 1500 Ω, C_{4} = 0.8 μF. Calculate R_{1}, L_{1} and Q factor, if the frequency is 1100 Hz.**

a) 240 Ω, 0.12 H, 3.14

**b) 140 Ω, 0.168 H, 8.29**

c) 140 Ω, 0.12 H, 5.92

d) 240 Ω, 0.36 H, 8.29

**Answer: b**

**Explanation: From Maxwell’s capacitance, we have**

**R**

_{1}= \(\frac{R_2 R_3}{R_4} = \frac{300 × 700}{1500}\) = 140 Ω**L**

_{1}= R_{2}R_{3}C_{4}**= 300 × 700 × 0.8 × 10**

^{-6}= 0.168 H**Q = \(\frac{ωL_1}{R_1} = \frac{2 × π × 1100 × 0.168}{140}\) = 8.29.**

**3. In Wein’s bridge, the output frequency is determined by __________**

a) RLC combination

b) LC combination**c) RC combination**

d) RL combination**Answer: c****Explanation: The frequency of Wien Bridge is given by****f = \(\frac{1}{2π(R_1 R_2 C_1 C_2 )^{0.5}}\) Hz****∴ The output frequency is determined by the RC combinations.**

**4. What is the disadvantage of Maxwell Bridge?****a) Inductance cannot be measured over a wide range**

b) Measurement is not independent of frequency

c) Number of components is large

d) Inductance can be measured over a wide range**Answer: a****Explanation: Maxwell Bridge cannot be used for the measurement of high Q values.****We have, Q = \(\frac{1}{ωR_X C_X} = \frac{ωL_X}{R_X}\)****Hence, Q ∝ L _{X}**

**∴ Inductance cannot be measured over a wide range.**

**5. The Bridge shown in the below figure is ______________****a) Maxwell’s Bridge**

b) Wien’s Bridge

c) Anderson’s Bridge

d) Hay’s Bridge**Answer: a****Explanation: The given figure is Maxwell’s Bridge because it consists of two inductors. It is also used to measure the inductance of the inductor.**

**6. Hay’s Bridge is used for measuring __________**

a) Resistance in the milliohm range

b) Low values of capacitance

c) Comparison of resistances which are nearly equal**d) The Inductance of a coil with a large time constant****Answer: d****Explanation: Carey – Foster slide-wire is suited for the comparison of resistances which are nearly equal. The Schering Bridge is suited for Low values of capacitance. The Kelvin double bridge is used for measuring resistance in the milliohm range. Hay’s Bridge is suited for the measurement of Inductance of a coil with a large time constant.**

**7. In Maxwell’s Bridge, as shown in the figure below, the values of the resistance R _{1} and inductance L_{1} of a coil are to be calculated after the bridge is balanced. The values are?**

**a) 375 Ω and 75 mH**

b) 75 Ω and 150 mH

c) 37.5 Ω and 75 mH

d) 75 Ω and 75 mH

**Answer: a**

**Explanation: Applying the usual balance condition relation,**

**Z**

_{1}Z_{4}= Z_{2}Z_{3}**We have, (R**

_{1}+ jL_{1}ω) \(\frac{R_4/jωC_4}{R_4+1/jωC_4}\) = R_{2}R_{3}**Or, R**

_{1}R_{4}+ jL_{1}ωR_{4}= R_{2}R_{3}+ j R_{2}R_{3}R_{4}C_{4}ω**∴ R**

_{1}= 2000 × \(\frac{750}{4000}\) = 375 Ω**∴ L**

_{1}= 2000 × 750 × 0.5 × 10^{-6}**= 75 mH.**

**8. Maxwell’s Inductance Capacitance Bridge is used for measuring ___________****a) Inductance**

b) Capacitance

c) Frequency

d) Mutual Inductance**Answer: a****Explanation: For measuring Capacitance De-Sauty’s Bridge and Schering Bridge should be used. For measuring Frequency Wien’s Bridge is used. For measuring Mutual Inductance Heaviside and Campbell’s Bridge are used.**

**9. The four arms of an AC bridge network are as follows:****Arm AB: unknown impedanceArm BC: standard capacitor C _{2} of 1000pfArm CD: a non-inductive resistance of R of 100 Ω in parallel to a capacitor of 0.01 μF**

**Arm DA: a non-inductive resistance of 1000 Ω**

**The supply frequency is 50 Hz and connected across terminals B and D. If the bridge is balanced with the above value, determine the value of unknown Impedance.**

**a) 10 kΩ**

b) 100 kΩ

c) 250 kΩ

d) 20 kΩ

**Answer: a**

**Explanation: For the balance conditions,**

**Z**

_{1}Z_{3}= Z_{2}Z_{4}**1000 × \(\frac{1}{jω × 1000 × 10^{-12}}\) = (R + jX) \(\frac{100}{1 + j100 × ω × 0.01 × 10^{-6}} \)**

**Or, \(\frac{10^{12}}{jω}\) = (R + jX) \(\frac{100}{1 + jω + 10^{-6}} \)**

**Or, \(\frac{- j10^{10}}{ω}\) – 10**

^{4}= R + jX**Comparing the real part, we get,**

**R = 10 kΩ.**

**10. The four arms of an AC bridge network are as follows:****Arm AB: unknown impedanceArm BC: standard capacitor C _{2} of 1000pfArm CD: a non-inductive resistance of R of 100 Ω in parallel to a capacitor of 0.01 μF**

**Arm DA: a non-inductive resistance of 1000 Ω**

**The supply frequency is 50 Hz and connected across terminals B and D. If the bridge is balanced with the above value, determine the value of unknown Capacitance.**

**a) 100 pf**

b) 1000 pf

c) 500 pf

d) 10 pf

**Answer: a**

**Explanation: For the balance conditions,**

**Z**

_{1}Z_{3}= Z_{2}Z_{4}**1000 × \(\frac{1}{jω × 1000 × 10^{-12}}\) = (R + jX) \(\frac{100}{1 + j100 × ω × 0.01 × 10^{-6}} \)**

**Or, \(\frac{10^{12}}{jω}\) = (R + jX) \(\frac{100}{1 + jω + 10^{-6}} \)**

**Or, \(\frac{- j10^{10}}{ω}\) – 10**

^{4}= R + jX**Comparing the imaginary part, we get,**

**\(\frac{1}{ωC} = \frac{10^{10}}{ω}\)**

**Or, C = 100 pf.**