Pre. year ques.
161 Term (1st Year 1st Semester)
1.¶
(a) State Gauss’s law. Deduce Coulomb’s law from Gauss’s law.
(b) Define electric dipole. What is the value of field \(\vec{E}\) due to positive and negative charges at point P?
(c) The distance between the electron and the proton in the hydrogen atom is about \(5 \times 10^{-11}\) m. What is the magnitude of the
(i) electric force, (ii) gravitational force between these two particles.
Compare the results. Consider the value of charge of the proton and electron is \(1.6 \times 10^{-19}\) C, mass of the electron \(m_e = 9.1 \times 10^{-31}\) kg; mass of the proton \(m_p = 1.7 \times 10^{-27}\) kg.
The gravitational constant \(G = 6.7 \times 10^{-11}\) N·m²/kg² and permittivity constant \(\varepsilon_0 = 8.854 \times 10^{-12}\) C²/N·m².
Marks: (2+4) + (1+3) + 4
2.¶
(a) What is electric circuit? Classify circuit parameters with their symbol and polarity.
(b) Distinguish between series and parallel circuits.
(c) In the circuit of the fig. below, calculate current supplied by the battery 6V.
(Diagram showing a combination of resistors: 0.2Ω in series, then splits into 2Ω, 3Ω, 6Ω)
Marks: 1+5, 3, 5
3.¶
(a) State and explain Kirchhoff’s laws.
(b) Make a comparison between voltage and current divider rules.
(c) In the circuit shown below apply KCL to find the value of current I for the case, when E = 2V.
(Diagram: 4Ω and 2Ω resistors in parallel, connected to a voltage source E)
Marks: 6, 4, 4
4.¶
(a) State and explain Thevenin’s Theorem. What do you understand by Thevenin’s source?
(b) Prove that \((P_L)_{max} = \frac{E_{th}^2}{4R_L}\), where \(R_L\), \(E_{th}\), and \((P_L)_{max}\) are the load resistance, Thevenin’s voltage and maximum power to the load respectively.
Marks: 4+1, 3
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(c) In the circuit shown in below, find the value of load resistance \(R_L\) to be connected across terminal A and B, which would receive maximum power from the circuit. Also find the value of the maximum power.
(Diagram: Combination of 3Ω, 4Ω, 6Ω resistors and RL between points A and B, 36V source)
Marks: 2+1
5.¶
(a) State and explain Superposition Theorem.
(b) Using Superposition theorem find the current through the 6Ω resistance of the network of Fig. below. Demonstrate that superposition is not applicable to power level.
(Diagram: R1 = 12Ω, R2 = 6Ω; two sources: 36V and 9V current source)
Marks: 4, 7+3
6.¶
(a) Make a comparison between DC and AC circuits.
(b) Mention some dissimilarity between magnetic and electric circuits.
(c) Prove that:
(i) \(I_{rms} = 1.11 I_{avg}\) for AC current.
(ii) \(I_{avg} = 0.637 I_m\)
Where \(I_{rms}\), \(I_{m}\) and \(I_{avg}\) are the root mean square value, the maximum value and average value of AC current respectively.
(d) An alternating current is represented by \(I = 141.4 \sin(628t)\). Calculate its
(i) frequency; (ii) RMS value; (iii) average value.
Marks: 3, 4, 2+2, 3
7.¶
(a) What do you understand by electrical resonance in AC series circuit and resonant frequency? Determine the resonant frequency.
(b) Describe resonance curve according to the variation of resistance. Define bandwidth of tuning circuit.
(c) An AC series R-L-C resonance circuit has resonance frequency of 2KHz and a Q-factor of 100.
Calculate:
(i) The bandwidth of the circuit;
(ii) Lower and upper half-power frequencies.
(d) If \(V_c\) is the voltage drop across capacitive reactance of AC R-L-C circuit and I is the current flowing through it, show the vector diagram of them.
Marks: 2+2, 3+2, 4, 1
**171 Term (1st Year 1st Semester) Final Examination**
1.¶
(a) Define electric field and electric field intensity. — 4
(b) State and explain Gauss’s law. Deduce Coulomb’s law from Gauss’s law. — 4+4
(c) What do you mean by electric dipole and dipole moment? — 2
2.¶
(a) Define the terms “Short” and “Open”. Explain “Short” and “Open” in a DC parallel circuit. — 2+4
(b) Write the conditions for connecting elements in
(i) series;
(ii) parallel. — 2+2
(c) Determine the unknown voltages \(V_1\) and \(V_2\) from the following figure-01. — 4
Figure-01: Circuit diagram with 24V source, 10V drop, 5V drop, R1 = 2.2kΩ, R2 = 5.6kΩ
3.¶
(a) State and explain Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL).
How do you determine the sign of voltage drops (IR)? — 4+2
(b) Make a comparison between voltage and current divider rules. — 2
(c) Using Kirchhoff’s current law and Ohm’s law, find the magnitude and polarity of voltage \(V\) in figure-02 shown below. — 5
Figure-02: Circuit with 2Ω, 5Ω, and 4Ω resistors, with 1A current source.
4.¶
(a) State and explain Thevenin’s theorem. What do you understand about Thevenin’s circuit and Thevenin’s source? — 4+2
(b) Define node and mesh. — 2
(c) Find the magnitude \(R_L\) for the maximum power transfer in the circuit shown in figure-03.
Also, find the maximum power. — 6
Figure-03: Circuit with 5Ω and 2Ω in parallel, 6A current source, and combination with 3Ω, 4Ω, and \(R_L\).
5.¶
(a) Draw a sinusoidal waveform and show amplitude, time period, cycle and peak-to-peak value of the curve. — 4
(b) Find the average value of the periodic waveform as shown in the figure-04. — 4
Figure-04: Sine waveform ranging from +10 to -15 with π interval markers.
(c) Draw the impedance triangle of the AC series R-L circuit and
(i) Find impedance;
(ii) Also find phase in terms of circuit parameters. — 3+3
6.¶
(a) Define bandwidth. Establish the relationship between bandwidth and quality factor of AC series RLC circuit. — 1+3
(b) State series resonance condition and determine resonance frequency of AC series RLC circuit. — 6
(c) Mention dissimilarities between electric and magnetic circuits. — 4
7.¶
(a) Make a comparison between AC series RLC and AC parallel RLC circuits. — 6
(b) Two impedances \(Z_1 = (8 + j6)\) and \(Z_2 = (3 - j4)\) are in parallel.
If the total current of the combination is 25A, find current taken by each impedance. — 8