Find the mean deviation about the mean for the following data
Question: Solution: Therefore $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}}$ $\frac{12500}{100}=125$...
Read More →A 60 W load is connected to the secondary of a transformer
Question: A 60 W load is connected to the secondary of a transformer whose primary draws line voltage. If a current of 0.54 A flows in the load, what is the current in the primary coil? Comment on the type of transformer being used. Solution: Ps = 60 W Is = 0.54 A Primary voltage = 220 V Vs = 60/0.54 = 110 V The transformer is a step-down transformer as the voltage in the secondary is less than the voltage in the primary. The transformation ratio is r = Vs/Vp = Ip/Is Substituting the values we g...
Read More →A coil of 0.01-henry inductance and 1-ohm
Question: A coil of 0.01-henry inductance and 1-ohm resistance is connected to 200 volt, 50 Hz ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current. Solution: Inductance L = 0.01 H Resistance R = 1 ohm Voltage = 200 V Frequency = 50 Hz Impedance = Z = 3.3 ohms Phase difference = 72 /180 rad Time lag in the alternating voltage and the current is 0.004 sec...
Read More →Both alternating current and direct current
Question: Both alternating current and direct current are measured in amperes. But how is the ampere defined for an alternating current? Solution: The ampere for an alternating current is defined in terms of the property known as Joules law of heating. According to Joules law of heating, AC is the current which is produced in the conductor when heat per second in the conductor is as direct current can produce in one-ohm resistance....
Read More →How does the sign of the phase angle φ,
Question: How does the sign of the phase angle , by which the supply voltage leads the current in an LCR series circuit, change as the supply frequency is gradually increased from very low to very high values. Solution: tan = Xl Xc/ R Xl Xc At resonate frequency, Xl = Xc tan = 0...
Read More →The alternating current in a circuit is described
Question: The alternating current in a circuit is described by the graph shown in Fig 7.4. Show rms current in this graph. Solution: The Irms = 1.6 A...
Read More →In series LCR circuit,
Question: In series LCR circuit, the plot of I max vs is shown in Fig 7.3. Find the bandwidth and mark in the figure. Solution: Frequency 1 = 0.8 rad/s Frequency 2 = 1.2 rad/s The bandwidth = 0.4 rad/s...
Read More →Can the instantaneous power output of an
Question: Can the instantaneous power output of an ac source ever be negative? Can the average power output be negative? Solution: (a) The instantaneous power output of the AC source can be negative when P 0 (b) The average power output cannot be negative as Pav 0....
Read More →Study the circuits (a) and (b) shown
Question: Study the circuits (a) and (b) shown in Fig 7.2 and answer the following questions. (a) Under which conditions would the rms currents in the two circuits be the same? (b) Can the rms current in the circuit (b) be larger than that in (a)? Solution: (a) (Irms)a = (Irms)b Xl = Xc R = R2+ (Xl Xc)2 Therefore, Irms will be equal in (a) as well (b) if Xl = Xc (b) For (Irms)b (Irms)a R2+ (Xl Xc)2 R (Xl Xc)2 0 Reactance cannot be negative....
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: we make the following table from the given data:br data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/22/image38624.png" alt="" Therefore, $\quad \overline{\mathrm{x}}=\frac{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{\circ} \mathrm{f}_{\mathrm{i}}}=\frac{12500}{100}=125$...
Read More →Draw the effective equivalent circuit of
Question: Draw the effective equivalent circuit of the circuit shown in Fig 7.1, at very high frequencies and find the effective impedance. Solution: The effective impedance = Zeq = R1 + R3...
Read More →Draw the effective equivalent circuit of
Question: Draw the effective equivalent circuit of the circuit shown in Fig 7.1, at very high frequencies and find the effective impedance. Solution: The effective impedance = Zeq = R1 + R3...
Read More →Evaluate the integral:
Question: Evaluate the integral: $\int \frac{x+1}{x^{2}+x+3} d x$ Solution: $I=\int \frac{x+1}{x^{2}+x+3} d x$ As we can see that there is a term of $x$ in numerator and derivative of $x^{2}$ is also $2 x$. So there is a chance that we can make substitution for $x^{2}+x+3$ and I can be reduced to a fundamental integration. As, $\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{2}+\mathrm{x}+1\right)=2 \mathrm{x}+1$ $\therefore$ Let, $x=A(2 x+1)+B$ $\Rightarrow x=2 A x+A+B$ On comparing both sides ...
Read More →If an LC circuit is considered analogous to a harmonically
Question: If an LC circuit is considered analogous to a harmonically oscillating spring block system, which energy of the LC circuit would be analogous to potential energy and which one analogous to kinetic energy? Solution: The magnetic energy of the LC circuit would be analogous to the kinetic energy while electrostatic energy due to change in charge of a capacitor would be analogous to the potential energy....
Read More →The line that draws power supply to your house from street has
Question: The line that draws power supply to your house from street has (a) zero average current. (b) 220 V average voltage. (c) voltage and current out of phase by 90. (d) voltage and current possibly differing in phase such that || /2. Solution: (a) zero average current. (d) voltage and current possibly differing in phase such that || /2....
Read More →When an AC voltage of 220 V is applied to the capacitor C
Question: When an AC voltage of 220 V is applied to the capacitor C (a) the maximum voltage between plates is 220 V. (b) the current is in phase with the applied voltage. (c) the charge on the plates is in phase with the applied voltage. (d) power delivered to the capacitor is zero. Solution: (c) the charge on the plates is in phase with the applied voltage. (d) power delivered to the capacitor is zero....
Read More →For an LCR circuit, the power transferred from the driving
Question: For an LCR circuit, the power transferred from the driving source to the driven oscillator is P = I2Z cos . (a) Here, the power factor cos 0, 0. P (b) The driving force can give no energy to the oscillator (P = 0) in some cases. (c) The driving force cannot syphon out (P 0) the energy out of oscillator. (d) The driving force can take away energy out of the oscillator. Solution: (a) Here, the power factor cos 0, 0. P (b) The driving force can give no energy to the oscillator (P = 0) in ...
Read More →Electrical energy is transmitted over large distances
Question: Electrical energy is transmitted over large distances at high alternating voltages. Which of the following statements is (are) correct? (a) For a given power level, there is a lower current. (b) Lower current implies less power loss. (c) Transmission lines can be made thinner. (d) It is easy to reduce the voltage at the receiving end using step-down transformers. Solution: (a) For a given power level, there is a lower current. (b) Lower current implies less power loss. (d) It is easy t...
Read More →In an alternating current circuit consisting of elements in series,
Question: In an alternating current circuit consisting of elements in series, the current increases on increasing the frequency of supply. Which of the following elements are likely to constitute the circuit? (a) Only resistor. (b) Resistor and an inductor. (c) Resistor and a capacitor. (d) Only a capacitor. Solution: (c) Resistor and a capacitor. (d) Only a capacitor....
Read More →As the frequency of an ac circuit increases,
Question: As the frequency of an ac circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit? (a) Inductor and capacitor. (b) Resistor and inductor. (c) Resistor and capacitor. (d) Resistor, inductor and capacitor. Solution: (a) Inductor and capacitor. (d) Resistor, inductor and capacitor....
Read More →The output of a step-down transformer is measured
Question: The output of a step-down transformer is measured to be 24 V when connected to a 12 watt light bulb. The value of the peak current is (a) 1/ 2 A. (b) 2 A. (c) 2 A. (d) 2 2 A Solution: (a) 1/ 2 A....
Read More →An inductor of reactance 1 Ω and a resistor of 2 Ω
Question: An inductor of reactance 1 Ω and a resistor of 2 Ω are connected in series to the terminals of a 6 V (rms) a.c. source. The power dissipated in the circuit is (a) 8 W. (b) 12 W. (c) 14.4 W. (d) 18 W. Solution: (c) 14.4 W....
Read More →Which of the following combinations
Question: Which of the following combinations should be selected for better tuning of an LCR circuit used for communication? (a) R = 20 Ω, L = 1.5 H, C = 35F. (b) R = 25 Ω, L = 2.5 H, C = 45F. (c) R = 15 Ω, L = 3.5 H, C = 30F. (d) R = 25 Ω, L = 1.5 H, C = 45F. Solution: (c) R = 15 Ω, L = 3.5 H, C = 30F....
Read More →To reduce the resonant frequency in an LCR
Question: To reduce the resonant frequency in an LCR series circuit with a generator (a) the generator frequency should be reduced. (b) another capacitor should be added in parallel to the first. (c) the iron core of the inductor should be removed. (d) dielectric in the capacitor should be removed. Solution: (b) another capacitor should be added in parallel to the first...
Read More →To reduce the resonant frequency in an LCR
Question: To reduce the resonant frequency in an LCR series circuit with a generator (a) the generator frequency should be reduced. (b) another capacitor should be added in parallel to the first. (c) the iron core of the inductor should be removed. (d) dielectric in the capacitor should be removed. Solution: (b) another capacitor should be added in parallel to the first...
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