**Electrical Measurements ****MCQs – ****Electronic Instruments ( ****Electrical Measurements ****) MCQs**

**Latest Electrical Measurements MCQs**

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**Electrical Measurements MCQs – Electronic Instruments ( Electrical Measurements ) MCQs**

The most occurred **mcqs of Electronic Instruments ( )** in past papers. **Past papers of Electronic Instruments ( Electrical Measurements )** Mcqs. **Past papers of** ** Electronic Instruments ( Electrical Measurements )** Mcqs . Mcqs are the necessary part of any competitive / job related exams. The Mcqs having specific numbers in any written test. It is therefore everyone have to learn / remember the related ** Electronic Instruments ( Electrical Measurements )** Mcqs. The Important series of ** Electronic Instruments ( Electrical Measurements ) Mcqs** are given below:

# Voltage to Frequency Converter Type Integrating DVM

**1. In a voltage to frequency converter type integrated DVM _____________****a) voltage is converted to time**

b) voltage is converted to frequency

c) frequency is converted to voltage

d) frequency is converted to time**Answer: a****Explanation: We know that the quantities time and frequency are related to each other. Voltage is converted into time in a voltage to frequency converter type integrating DVM.**

**2. Input voltage is measured by ____________**

a) using a voltmeter**b) counting pulses**

c) using a multimeter

d) using an ammeter**Answer: b****Explanation: A pulse train is generated. Their frequency depends on the frequency of the unknown voltage. Number of pulses present in a definite interval are counted. Unknown input voltage is a measure of the pulses generated.**

**3. What is the main component of an integrating type DVM?**

a) diode

b) amplifier**c) op amp**

d) oscillator**Answer: c****Explanation: An op amp forms the heart of the integrating type DVM. Op amp is used as an integrator. The input signal is integrated for a fixed interval giving rise to a ramp signal at the output.**

**4. When input is positive, then output is?**

a) growing exponential signal

b) decaying exponential signal

c) positive going ramp**d) negative going ramp****Answer: d****Explanation: The op amp produces a negative going ramp signal for a positive input voltage. Capacitor is discharged after some time and the output returns to zero. The next cycle starts and the output is a sawtooth waveform. Figure shows the output sawtooth waveform. **

**5. What is the effect of the input signal on the output teeth?****a) directly proportional**

b) inversely proportional

c) independent

d) square proportional**Answer: a****Explanation: When the input signal in a voltage to frequency conversion type integrated DVM is doubled, the number of tooth in the output signal is doubled per unit time. This doubles the frequency of the output signal.**

**6. Sawtooth pulses enter into a reversible counter.****a) True**

b) False**Answer: a****Explanation: The sawtooth output signal obtained from the integrating type DVM is passed through a reversible counter. A digital readout displays the value measured by the reversible counter.**

**7. Application of an input voltage generates a ____________**

a) linear signal at the output**b) ramp at the output**

c) exponential signal at the output

d) unit step signal at the output**Answer: b****Explanation: When an input voltage of magnitude Vin is applied at the input, capacitor C is charged by the charging current Vin/R1. As a result a ramp signal is produced at the output.**

**8. Number of pulses is related to frequency.****a) True**

b) False**Answer: a****Explanation: Each tooth in the sawtooth waveform produces a pulse at the output of the pulse generator. Hence the number of tooth i.e. the frequency is directly related to the number of pulses.**

**9. Accuracy depends on ____________**

a) input voltage

b) drop across the capacitor**c) magnitude and stability of pulse generator**

d) magnitude of the ramp**Answer: c****Explanation: Accuracy of the voltage to frequency conversion depends on the capacity of the pulse generator to produce an electric charge with a suitable magnitude and stability. Hence the accuracy depends on the precision of the charge feedback.**

**Potentiometric Integrating Type DVM**

**1. In a potentiometric DVM ________****a) voltage is compared**

b) current is compared

c) resistance is compared

d) power is compared**Answer: a****Explanation: Potentiometric integrating type DVM employs voltage comparison. The unknown voltage is compared with a reference. The reference value is set by a calibrated potentiometer.**

**2. How to obtain balance?**

a) by using a detector**b) by changing the pot setting**

c) by supplying voltage

d) by using a transformer**Answer: b****Explanation: Balance is obtained in a potentiometric integrating type DVM by adjusting the settings of the potentiometer. The dial setting of the potentiometer gives the value of the unknown voltage.**

**3. In a potentiometric DVM, balance is obtained manually.**

a) True**b) False****Answer: b****Explanation: Balance is obtained in a potentiometric integrating type DVM by adjusting the settings of the potentiometer. Hence in a potentiometric integrating type DVM, the balance is obtained automatically.**

**4. Unknown voltage is __________**

a) converted to current

b) boosted**c) filtered**

d) measured using a voltmeter**Answer: c****Explanation: In a potentiometric integrated type DVM, the unknown voltage is filtered. It is also attenuated to a suitable magnitude. This forms the input for the comparator. A chopper is usually used as an error detector.**

**5. How is the reference voltage obtained?**

a) from a fixed current source

b) from a variable voltage source

c) from a variable current source**d) from a fixed voltage source****Answer: d****Explanation: Reference voltage is applied to the potentiometer. It is obtained from a source of fixed voltage. The position of the slider on the contact surface determines the value of the feedback voltage.**

**6. Feedback voltage is applied to the ________****a) comparator**

b) error amplifier

c) potentiometer

d) sliding contact**Answer: a****Explanation: Comparator accepts the feedback voltage as an input. Comparator compares the values of the unknown voltage and the feedback voltage. Comparator then provides the difference between the feedback voltage and the unknown voltage as its output.**

**7. Output of the comparator is known as ________**

a) amplified signal**b) error signal**

c) feedback signal

d) attenuated signal**Answer: b****Explanation: Comparator then provides the difference between the feedback voltage and the unknown voltage as its output. This is also known as the error signal.**

**8. Slider movement depends on ________**

a) current magnitude

b) resistance magnitude**c) voltage magnitude**

d) power magnitude**Answer: c****Explanation: In a potentiometric integrating type DVM, the slider moves based on the magnitude of the feedback voltage with respect to the input voltage. Contact is pushed back to the place where the unknown voltage equals the feedback voltage.**

**9. Accuracy of a potentiometric DVM is ________**

a) zero

b) medium

c) low**d) high****Answer: d****Explanation: In a potentiometric integrating type DVM, the accuracy is usually high. It generally depends on the reference of the digital to analog converter. Accuracy of the voltage to frequency converter is less important compared to that of the digital to analog converter.**

**Dual Slope Integrating Type DVM**

**1. Why is dual slope method preferred over ramp techniques?****a) no noise**

b) partial noise

c) average noise

d) maximum noise**Answer: a****Explanation: During the process of integration, noise is canceled out by the positive and negative ramps in the dual slope method. The input signal is integrated only for a fixed interval of time and this is the basis for the dual slope method.**

**2. What is the significance of the name dual slope method?**

a) it has two slopes**b) it integrates the input twice**

c) it uses two inputs

d) it has two outputs**Answer: b****Explanation: The input signal is integrated only for a fixed interval of time and this is the basis for the dual slope method. Reference voltage is integrated with a negative slope. Hence the method is known as dual slope integrating type DVM.**

**3. What is the output voltage in a dual slope integrating type DVM?**

a) differential of the input

b) multiple of the input**c) integral of the input**

d) zero**Answer: c****Explanation: In a dual slope integrating type DVM, the output voltage is given by the integral of the input voltage.****where, V _{in} is the input voltage**

**R**

_{1}is the series resistance**t**

_{1}is the time for which the capacitor is charged.**4. Input voltage depends on ____________**

a) resistance

b) capacitance

c) current**d) time-period****Answer: d****Explanation: The input voltage in a dual slope integrating type DVM is given by the relation,****V _{in} = V_{ref} ^{t2} ⁄ _{t1}**

**From the above equation it is seen that the input voltage in a dual slope integrating type DVM depends on the time periods t**

_{1}for which the capacitor is charged and t_{2}during which the capacitor is discharged.**5. Noise rejection is poor.**

a) True**b) False****Answer: b****Explanation: In a dual slope integrating type DVM, the noise is cancelled out by the positive and negative ramps during the process of integration. As a result, the noise rejection is excellent.**

**6. What is the effect of the capacitor on the output?****a) no effect**

b) charging effect

c) electrostatic effect

d) magnetic effect**Answer: a****Explanation: In the dual slope integrating type DVM method, the capacitor is connected through means of an electronic switch. As a result the effects due to offset voltage wherein there exists an output voltage without the application of any input are eliminated.**

**7. What is the effect of clock on the voltage?**

a) voltage doubles with clock input

b) voltage halves with clock input**c) no effect**

d) voltage becomes zero with clock input**Answer: c****Explanation: In a dual slope integrating type DVM, the value of the unknown voltage is independent of the frequency of the clock. It depends only on the number of counts read by the electronic counter.**

**8. What is the counter value at the beginning?**

a) one

b) ten

c) three**d) zero****Answer: d****Explanation: In a dual slope integrating type DVM, the electronic counter is reset to 0 at the beginning of the measurement of voltage. Flip-flop output is also maintained at zero and is given to control logic.**

**9. What is the maximum count of the counter?****a) 9999**

b) 0

c) 500

d) 1000**Answer: a****Explanation: In a dual slope integrating type DVM, the electronic counter reaches a maximum value of 9999 before resetting. A carry pulse is generating pulling down all the digits to zero. Flip-flop then activates the control logic.**

**Resolution and Sensitivity**

**1. Resolution of a DVM is given by ____________****a) R = ^{1}⁄_{10n}**

b) R = 1

c) R = 10

^{n}

d) R =

^{n}⁄

_{10}

**Answer: a**

**Explanation: The resolution of a DVM is,**

**R =**

^{1}⁄10^{n}**where, n is the number of full digits**

**R is the resolution.**

**2. What is the resolution for a 3 digit display?**

a) 1 %**b) 0.1 %**

c) 0.001 %

d) 10 %**Answer: b****Explanation: The resolution of a DVM is,****R = ^{1}⁄_{10n}**

**Here, n is 3. Substituting n=3 in the equation for resolution we get,**

**R =**

^{1}⁄_{103}= 10^{-3}= 0.001 = 0.1 %.**3. Sensitivity is largest change in input.**

a) True**b) False****Answer: b****Explanation: Sensitivity of any instrument is defined as the smallest hange in the input signal to which the output responds.**

**4. Sensitivity of a DVM is given by ______________**

a) S = 1

b) S = (fs)_{min}**c) S = (fs) _{min} × R**

d) S = R

**Answer: c**

**Explanation: Sensitivity of the DVM is obtained from the relation,**

**S = (fs)**

_{min}× R**where, S is the sensitivity**

**R is the resolution**

**(fs)**

_{min}is the full scale value on minimum range.**5. What is the resolution of a 3 digit display on 1 V range?**

a) 1 V

b) 0.1 V

c) 0.01 V**d) 0.001 V****Answer: d****Explanation: The resolution of a DVM is,****R = ^{1}⁄_{10n}**

**Here, n is 3. Substituting n=3 in the equation for resolution we get,**

**R =**

^{1}⁄_{103}= 10^{-3}= 0.001**For 1 V range, the resolution is,**

**R**

_{1V}= 1×0.001 = 0.001 V.**6. How is 11.87 V displayed on a 10 V range for a 4 digit display?****a) 11.870**

b) 1.1870

c) 118.7

d) 0.1187**Answer: a****Explanation: The resolution of a DVM is,****R = ^{1}⁄_{10n}**

**Here, n is 4. Substituting n=4 in the equation for resolution we get,**

**R =**

^{1}⁄_{104}= 10^{-4}= 0.0001**Since there are 5 digit places in the resolution, 11.87 which already has four digits is represented as 11.870.**

**7. Consider a 3 digit display for a DVM with an accuracy of ± 0.5 % for a reading of ± 1 digit. Compute the error for 5 V reading on a 10 V range.**

a) ± 10 V**b) ± 0.035 V**

c) ± 0.05 V

d) ± 1 V**Answer: b****Explanation: The resolution of a DVM is,****R = ^{1}⁄_{10n}**

**Here, n is 3. Substituting n=3 in the equation for resolution we get,**

**R =**

^{1}⁄_{103}= 10^{-3}= 0.001**For 10 V range, the resolution is,**

**R**

_{10V}= 10 × 0.001 = 0.01 V**Consider the reading of 5 V.**

**Error = ± 0.5 % of 5 =**

^{0.5}⁄_{100}× 5 = ± 0.025 V**1 digit error = ± 0.01 V**

**Total error = ±(0.025 V+ 0.01 V)=± 0.035 V.**

**8. Clock pulses are controlled ______**

a) automatically

b) using microcontrollers

c) using valves**d) manually****Answer: d****Explanation: A manual range hold command is used to control the clock pulses and the autoranging. This is done through a signal that exceeds the maximum range for up counts by reaching the most sensitive range (down counts).**

**Autoranging**

**1. Autoranging means __________****a) automatic ranging**

b) fixed ranging

c) automobile ranging

d) constant ranging**Answer: a****Explanation: Autoranging refers to obtaining an automatic reading with optimum resolution under all operating conditions. Say for example, 155 mV is displayed as 155.0 and not 0.155.**

**3. For a value less than 0200, the instrument should ________**

a) read values less than 0200 correctly

b) read values randomly**c) automatically switch range**

d) should not respond at all**Answer: c****Explanation: The DVM should automatically switch its range when the display is greater than 1999 units as it is the maximum set limit for achieving a higher sensitivity.**

**4. ADC counter ________**

a) attenuates the signal

b) converts digital to analog

c) converts analog to digital**d) contains information****Answer: d****Explanation: When the count produced by the ADC counter is less than 170, a control pulse is obtained for down ranging. Whereas the control pulse for up ranging is produced once the ADC counter exceeds 1999 units.**

**5. ADC gives polarity indication.****a) True**

b) False**Answer: a****Explanation: ADC contains information required for polarity indication. The polarity of the signal that is integrated is of utmost importance.**

**6. Integration period is obtained by ________**

a) using signal amplitude**b) counting the pulse**

c) measuring time

d) by differentiating the signal**Answer: b****Explanation: By counting the pulses we obtain the integration period. Polarity measurement is obtained by making use of the last count or some of the last counts.**

**7. Integrator’s output is ________**

a) attenuated through a filter

b) feedback to the input**c) stored in a flip-flop**

d) differentiated**Answer: c****Explanation: The output from the integrator is used to set a polarity flip-flop. The flip-flop’s output is then stored in memory until the next measurement of voltage is obtained.**

**8. Old information is used to set range relays.**

a) True**b) False****Answer: b****Explanation: Range relays are set through the decoder using the new information obtained with the help of a clock pulse. Decimal point is also changed as per the requirement of the new range.**

**Digital Multimeter**

**1. Digital multimeter is used for _________****a) measuring a.c. and d.c. current, voltage and resistance**

b) measuring a.c. current and voltage

c) measuring d.c. current and resistance

d) measuring a.c. voltage and resistance**Answer: a****Explanation: Digital multimeter is usually used for the measurement of a.c. current, voltage and resistance. It is also used for the measurement of d.c. current, voltage and resistance as well over several range.**

**2. Current is converted to voltage __________**

a) through a voltmeter**b) through a resistance**

c) through an ammeter

d) through a galvanometer**Answer: b****Explanation: Current is passed through a low shunt resistance and is converted to voltage. A.C. quantities are converted to D.C. through various rectifier and filter circuits. Voltmeter and ammeter are used for voltage and current measurement respectively.**

**3. For resistance measurement, meter contains _________**

a) high current source

b) medium current source**c) low current source**

d) low voltage source**Answer: c****Explanation: Usually in the measurement of resistance, meter consists of a precision low current source applied across an unknown resistance which gives a d.c. voltage.**

**4. Quantities are digitised using _________**

a) D/A converter

b) oscillator

c) amplifier**d) A/D converter****Answer: d****Explanation: Quantities such as current, voltage and resistance are digitised by making use of an A/D converter. They are then displayed on the screen by making use of a digital display.**

**5. Analog multimeters require power supply.**

a) True**b) False****Answer: b****Explanation: Analog multimeters are less affected by electric noise and isolation problems. As a result analog multimeters don’t require a power supply.**

**6. Output of a digital multimeter is _________**

a) mechanical

b) optical**c) electrical**

d) analog**Answer: c****Explanation: Digital multimeter gives an electrical signal as the output. A/D converter is employed for the conversion from analog to digital signal. This can be used for interfacing with external equipment.**

**7. Basic building blocks of digital multimeter are _________**

a) oscillator, amplifier

b) diode, op amp

c) rectifier, schmitt trigger**d) A/D, attenuator, counter****Answer: d****Explanation: Usually dual slope integrating type ADC is preferred in multimeter. It basically consists of several A/D converters, counter circuits and an attenuation circuit.**

8. Resistance is measured using _________

a) constant current source

b) constant voltage source

c) variable current source

d) variable voltage source**Answer: a****Explanation: Constant current source is used to measure resistance in a digital multimeter. Standard known value of current is passed through an unknown resistance and the drop in voltage across the resistance is measured.**

**9. A.C. voltages are measured using _________**

a) oscillators and op amps**b) rectifiers and filters**

c) resistor and capacitor

d) inductor and resistor**Answer: b****Explanation: Rectifiers and filter circuits with various configurations are employed for measuring A.C. voltages. A.C. is converted to D.C. and is applied to the A/D converter.**

**Qmeter**

**1. Q factor is called __________****a) Quality factor**

b) Quantity factor

c) Queen factor

d) Quarter factor**Answer: a****Explanation: Q factor is also known as Quality factor or storage factor. It is basically a ratio of the power stored in an element to the power dissipated in that element.**

**2. Q factor is also defined as the ratio of _______**

a) resistance to reactance**b) reactance to resistance**

c) power to voltage

d) current to power**Answer: b****Explanation: Q factor can also be obtained as the ratio of reactance to resistance of an element. For inductive element it is the ratio of X _{L} to R and for a capacitive element it is the ratio of X_{C} to R.**

**3. What is a Q meter?**

a) quality meter

b) quantity meter**c) instrument**

d) detector**Answer: c****Explanation: Q meter is basically an instrument that is used for the measurement of electrical properties of capacitors and coils. It is also used as a laboratory instrument.**

**4. Q meter works on the principle of _______**

a) barkhausen criterion

b) piezoelectric effect

c) parallel resonance**d) series resonance****Answer: d****Explanation: Q meter basically operates on the characteristics of a series resonant coil. In a series resonant circuit the voltage drop across the coil or a capacitor is equal to the applied voltage multiplied by its Q factor.**

**5. Q factor for a series resonant circuit is?****a) Q = \(\frac{X_L}{R} = \frac{X_C}{R}\)**

b) Q = X_{L} R = X_{C} R

c) Q = \(\frac{R}{X_L} = \frac{R}{X_C}\)

d) Q = \(\frac{1}{R}\)**Answer: a****Explanation: Q factor in a series resonant circuit is given by the relation,****Q = \(\frac{X_L}{R} = \frac{X_C}{R}\)****where, R is resistance of the coil****X _{C} is the capacitive reactance**

**X**

_{L}is the inductive reactance.**6. What is the relation between Q factor and voltage?**

a) Q = \(\frac{1}{E}\)**b) Q = \(\frac{X_L}{R}=\frac{X_C}{R}=\frac{E_C}{E}\)**

c) Q = E

d) Q = \(\frac{R}{X_L}=\frac{R}{X_C}=\frac{E}{E_C}\)**Answer: b****Explanation: The applied voltage E is inversely proportional to the Q factor of a circuit and is given by the relation,****Q = \(\frac{X_L}{R}=\frac{X_C}{R}=\frac{E_C}{E}\).**

**7. A practical Q meter consists of __________**

a) Wien bridge oscillator

b) AF oscillator**c) RF oscillator**

d) Crystal oscillator**Answer: c****Explanation: Practically a Q meter consists of a wide range RF oscillator with a frequency range of 50 kHz to 50 MHz. Oscillator acts as a source and delivers current to a low shunt resistance.**

**8. Voltage across the shunt is measured by ________**

a) voltmeter

b) multimeter**c) thermocouple**

d) thermometer**Answer: c****Explanation: A thermocouple is used for measuring the voltage across a shunt resistance in a practical Q meter. Electronic voltmeter is used for the measurement of voltage across a resonant capacitor.**

**9. Inductance of the coil is ________**

a) L = \(\frac{1}{(2πf)C}\)

b) L = \(\frac{1}{(2πf)^2}\)

c) L = \(\frac{1}{C}\)**d) L = \(\frac{1}{(2πf)^2 C}\)****Answer: d****Explanation: Coil inductance in a Q meter is given by the relation,****L = \(\frac{1}{(2πf)^2 C}\)****where, f is the frequency in Hz****C is the capacitance in F.**

**Advanced Problems on Q Meter**

**1. Q meter operator is the principle of __________****a) Series resonance**

b) Current resonance

c) Self-inductance

d) Eddy currents**Answer: a****Explanation: We know that Q = \(\frac{ωL}{R}\)****From the above relation, we can say that it works on series resonance.**

**2. In a Q Meter, the values of tuning capacitor are C _{3} and C_{4} for resonant frequencies f_{3} and 2f_{4} respectively. The value of distributed capacitance is?**

a) \(\frac{C_3-C_4}{2}\)

b) \(\frac{C_3-2C_4}{3}\)

**c) \(\frac{C_3-4C_4}{3}\)**

d) \(\frac{C_3-3C_4}{2}\)

**Answer: c**

**Explanation: Q**

_{X}= \(\frac{R_P}{X_P} = \frac{(C_4 – C_3)Q_3 Q_4}{Q_3 C_3 – Q_4 C_4}\)**The main error in the measurement of Q is due to the distribution. To check for this, the Q value is measured at two frequencies f**

_{1}and 2f_{2}. It should be same, if not then, \(\frac{C_3-4C_4}{3}\).**3. A circuit tuned to a frequency of 1.5 MHz and having an effective capacitance of 150 pF. In this circuit, the current falls to 70.7 % of its resonant value. The frequency deviates from the resonant frequency by 5 kHz. Q factor is?**

a) 50

b) 100**c) 150**

d) 200**Answer: c****Explanation: Q = \(\frac{ω}{ω1 – ω2} = \frac{f}{f2-f1}\)****Here, f = 1.5 × 10 ^{6} Hz**

**f1 = (1.5 × 10**

^{6}– 5 × 10^{3})**f2 = (1.5 × 10**

^{6}+ 5 × 10^{3})**So, f2 – f1 = 10 × 10**

^{3}Hz**Q = \(\frac{1.5 × 10^6}{10 × 10^3}\) = 150.**

**4. A circuit tuned to a frequency of 1.5 MHz and having an effective capacitance of 150 pF. In this circuit, the current falls to 70.7 % of its resonant value. The deviates from the resonant frequency are 5 kHz. Effective resistance of the circuit is?**

a) 2 Ω

b) 3 Ω

c) 5.5 Ω**d) 4.7 Ω****Answer: d****Explanation: R = \(\frac{f2-f1}{2πf^2 L}\)****Here, f = 1.5 × 10 ^{6} Hz**

**f1 = (1.5 × 10**

^{6}– 5 × 10^{3})**f2 = (1.5 × 10**

^{6}+ 5 × 10^{3})**So, f2 – f1 = 10 × 10**

^{3}Hz**R = \(\frac{10 × 10^3}{2π(1.5 × 10^6)^2 L}\)**

**R = 4.7 Ω.**

**5. Q Meter is used to measure _________**

a) Q factor of an inductive coil

b) Only the effective resistance

c) Only bandwidth**d) Q factor of an inductive coil, the effective resistance, and bandwidth****Answer: d****Explanation: Q meter can measure the Q factor of an inductive coil. It can also measure the effective resistance. Also, the bandwidth can be measured by the Q Meter. Therefore it can be used for all the above functions.**

**6. Q factor of a coil measured by the Q Meter is _________ the actual Q of the coil.**

a) Equal to**b) Same but somewhat lesser than**

c) Same but somewhat higher than

d) Not equal to**Answer: b****Explanation: The Q factor measured by the Q meter cannot be exactly equal to the actual Q of the coil because of the presence of errors. Also, it is not practically possible for the value to be higher than the actual one. But the value is somewhat lesser and almost equal to the actual value.**

**7. Consider a circuit consisting of two capacitors C _{1} and C_{2}. Let R be the resistance and L be the inductance which are connected in series. Let Q_{1} and Q_{2} be the quality factor for the two capacitors. While measuring the Q value by the Series Connection method, the value of the Q factor is?**

**a) Q = \(\frac{(C_1 – C_2 ) Q_1 Q_2}{Q_1 C_1 – Q_2 C_2}\)**

b) Q = \( \frac{(C_2 – C_1 ) Q_1 Q_2}{Q_1 C_1 – Q_2 C_2}\)

c) Q = \( \frac{(C_1 – C_2 ) Q_1 Q_2}{Q_2 C_2 – Q_1 C_1}\)

d) Q = \( \frac{(C_2 – C_1 ) C_1 C_2}{Q_1 C_1 – Q_2 C_2}\)

**Answer: a**

**Explanation: ωL = \(\frac{1}{ωC}\)and Q**

_{1}= \(\frac{ωL}{R} = \frac{1}{ωC_1 R}\)**X**

_{S}= \(\frac{C_1-C_2}{ωC_1 C_2 }\), R_{S}= \(\frac{Q_1 C_1 – Q_2 C_2}{ωC_1 C_2 Q_1 Q_2}\)**Q**

_{X}= \(\frac{X_S}{R_S} = \frac{(C_1- C_2) Q_1 Q_2}{Q_1 C_1-Q_2 C_2}\).**8. Consider a circuit consisting of two capacitors C _{1} and C_{2}. Let R be the resistance and L be the inductance which are connected in series. Let Q_{1} and Q_{2} be the quality factor for the two capacitors. While measuring the Q value by the Parallel Connection method, the value of the Q factor is?**

a) Q = \(\frac{(C_1 – C_2 ) Q_1 Q_2}{Q_1 C_1 – Q_2 C_2}\)

**b) Q = \(\frac{(C_2 – C_1 ) Q_1 Q_2}{Q_1 C_1 – Q_2 C_2}\)**

c) Q = \(\frac{(C_1 – C_2 ) Q_1 Q_2}{Q_2 C_2 – Q_1 C_1}\)

d) Q = \(\frac{(C_2 – C_1 ) C_1 C_2}{Q_1 C_1 – Q_2 C_2}\)

**Answer: b**

**Explanation: \(\frac{1}{R_P} = \frac{ωC_1}{Q_2} – \frac{1}{RQ_1^2}\), X**

_{P}= \(\frac{1}{ω(C_2 – C_1)}\)**Q = \(\frac{(C_2 – C_1 ) Q_1 Q_2}{Q_1 C_1 – Q_2 C_2}\).**

**9. Consider the following statements regarding the sources of error in a Q Meter.****i) If a coil with a resistance R is connected in the direct measurement mode andIf the residual resistance of the Q Meter is 0.1 R, Then the measured Q of the coil would be 1.1 times the actual Q.ii) If the inductance to be measured is less than 0.1 μH.The error due to the presence of residual inductance cannot be neglected.**

**iii) The presence of a distributed capacitance modifies the effective Q of the coil.**

**Which of the above statements are correct?**

a) i, ii and iii

b) i and ii

**c) ii and iii**

d) i and iii

**Answer: c**

**Explanation: We know that, Q = \(\frac{Lω}{R}\)**

**With Q Meter resistance considered, the measured or indicated Q is 1/1.11 times the actual Q. Thus, statement (i) is incorrect. Hence, statements (ii) and (iii) are correct.**

**10. The function of the Q- Meter is to _________**

a) Measure capacitance

b) Measure inductance**c) Measure quality factor of capacitor and inductor**

d) Measure form factor of capacitor and inductor**Answer: c****Explanation: Q-Meters are intended to measure the quality factor of a capacitor and inductor. Q = \(\frac{Lω}{R} = \frac{1}{ωCR} = \frac{V_C}{V_A}\). They are not used for measuring capacitances and inductances, unlike AC Bridges.**